Histories

The following version of the pedigree of Sir William has been traced to a file held in the Society of Scottish Genealogy Society's Family Tree Collection and listed in their Family History Index.
It is oft quoted and contains several connections now known to be errors of fact, together with a number of leads for further investigation (my comments/notes in brackets).
Representatives for any of the lines shown would be most welcome to join the project to add modern technology to the historical document and aid in building an accurate overall Fairbairn pedigree.
John Fairbairn, b. 1563 m 1585
└── John Fairbairn, b. 1585 m 1610 d 1645 stone in Ednam (see * below)
     └──Robert Fairbairn, b. 1611 m 1636
          └── John Fairbairn, b. 1637 m 1662
                └── Robert Fairbairn, b. 1662 m 1683 d 1697 stone in Ednam (see * below)
                     └── John Fairbairn, b. 1688  m. 1713
                          ├── John Fairbairn, b. 1714 ROX, SCT d 1797 Galashiels (See LIneage2b for pedigree of John Fairbairn and Helen Anderson)
                          │   m1 1745 Lucy Eadster
                          │  ├── Robert Fairbairn, b. 1749 m 1772 d 1829
                          │  ├── Thomas Fairbairn, b. 1751
                          │  └── John Fairbairn, b. 1753 Makerston m 1776 Elizabeth Yule 1824 to Ontario d 1830 Darlington Ontario Family pioneers in Brockville, Teeswater
                          │   m2 1754 Helen Anderson (See LIneage2b above for pedigree of John Fairbairn and Helen Anderson, who married 1748)
                          │  ├── Walter Fairbairn, b. 1755 d 1755 
                          │  ├── William Fairbairn, b. 1756  m Margaret Thomson d 1809 Family Dr John Mayo Clinic  (see pedigree for the Ednam blacksmiths)
                          │  ├── Andrew Fairbairn, b. 1758 Smailholm, ROX, SCT m 1783 Margaret Henderson d 1844 Surrey 
                          │  │    └── Sir William Fairbairn 1st Baronet, b. 1789
                          │  └── Peter Fairbairn, b. 1769 m 1785 d 1828 Barbados
                          │       └── Sir Peter Fairbairn, b. 1799 (See LIneage2b  for pedigree of John Fairbairn and Helen Anderson)
                          ├── Robert Fairbairn, b. 1716 m 1744 d 1800
                          ├── Thomas Fairbairn, b. 1719
                          ├── James Fairbairn, b. 1720
                          ├── Isobel Fairbairn, b. 1722
                          ├── George Fairbairn, b. 1724 m 1746 d 1789
                          ├── Agnes Fairbairn, b. 1726 m 1747
                          ├── Patrick Fairbairn, b1728 m 1762 Margaret Purvis d 1790 (to John of Haliburton m. Jessie Johnston)
                          └── Margaret Fairbairn, b. 1729 m 1751 Hall
* The stones in Ednam may well have been legible in years past, but those above are no longer evident.
The booklet "Roxburghshire monumental Inscriptions VI Ednam" does not contain any FAIRBAIRN stones that early. It does however contain the stones relating to the Ednam blacksmith family referred to below.
However, new information to hand has an interesting variant on these "stones in Ednam" references in that it says "live{d?} Gravestone, Ednam".
If anyone knows of such a place please contact the administrator (links below). As to which is correct, headstone in Ednam or a place that may be an interpretation of gravestone in Ednam, don't know.
Should anyone come across earlier transcriptions of those referred to above please send an email to the Project Administrator with the details.
Those interested in how the assorted pedigrees of these families, differ, or may relate, may be interested in the "Hit or Myth?" page under development on the Supplementary FAIRBAIRN dna pages.

An alternate version, author unknown, follows, and also contains the "stone in Ednam" and "Crest" references.  Does anyone know who published it? And when? The only two branches with further data are those of brothers John 1714 and Robert 1716.
John Fairbairn, b. 1563 m 1585
└──John Fairbairn, b. 1585 m 1610 d 1645 stone in Ednam (see * above)
     └── Robert Fairbairn, b. 1611 m 1636
          └── John Fairbairn, b. 1637 m 1662
                └── Robert Fairbairn, b. 1662 m 1683 (possibly twice) d stone in Ednam (see * above)
                     ├── Robert Fairbairn, b. 1680 d 1682
                     ├──  Isobel Fairbairn, b. 1684 m 1702 James Brown
                     └── John Fairbairn, b. 1688  m. 1713 (9 children)
                          ├── John Fairbairn, b. 1714 Nenthorn, BEW d 1797 
                          │    m1 1748 Helen Anderson
                          │    m2 ?
                          ├──  Robert Fairbairn, b. 1716 m 1744 d 1800 (with further details of the James & Helen (Goodfellow) line)
                          ├── Thomas Fairbairn, b. 1718 
                          ├── James Fairbairn, b. 1720
                          ├── Isobel Fairbairn, b. 1722
                          ├── George Fairbairn, b. 1724 m 1746 d 1789
                          ├── Agnes Fairbairn, b. 1726 m 1747 Patrick Crawford
                          ├── Patrick Fairbairn,  annotated "Australian descendants of Fairbairn line" (see Project diary Patrick or James? for additional comments/links/info)
                          └── Margaret Fairbairn, b. 1729 m 1751 James Hall

Yet another version, also contains the "stone in Ednam" references, also contains a number of errors of fact, and an interesting lead or two.  
This is taken from a 3 page document in the Wellington County, Ontario archives, there when the file was catalogued in 1994, sourced to a Nora CARLAW, now deceased. (nee MARSTON, granddtr of Clarissa Harlow FAIRBAIRN.)
The comments in red are taken from the file, but linked people take you to a page for the person concerned with some extra notes and commentary as the tree contains at least seven different family lines, not currently known to be linked as shown, although dna evidence to date does indicate several are related. (Representatives of the other lines included would be most welcome to help complete the jigsaw, comments in teal are some corrective notes)


John Fairbairn  b. 1503 (suspect a typo for 1563) mentions saving King James 1st & 6th, and a fief of land
└── John Fairbairn  b. 1585 (stone in Ednam)
     └── Robert Fairbairn, b. 1611
          └── John Fairbairn, b. 1637
               └── Robert Fairbairn b. 1662  (stone in Ednam)
                    ├── Robert Fairbairn, b. 1680
                    ├── Isobel Fairbairn, b. 1684 m. 1702 James Town
                    └── John Fairbairn, b. 1688
                         ├── John Fairbairn b. 1714 (these two marriages are to different Johns)
                         │   + 1748 Lucy Eadster
                         │   ├── Robert Fairbairn, b. 1749 Smailholm, ROX, SCT
                         │   └── Thomas Fairbairn, b. 1751 Smailholm, ROX, SCT  (Merchant in Berwick, mercer or dry goods)
                         │   + 1754 Helen Anderson
                         │   ├── John Fairbairn, b. 1755 Smailholm, ROX, SCT m. 1776 Shannabank Farm, BEW, SCT Elizabeth Yule (John d. Darlington, Canada)
                         │   │   ├── Robert Fairbairn, b. 1783
                         │   │   ├── Mary Fairbairn, b. 1785
                         │   │   ├── Edward Fairbairn, b. 1787
                         │   │   ├── Margaret Fairbairn, b. 1790
                         │   │   ├── John Fairbairn  b. 1792 m. 1816 Jane Williamson (belongs to the William supposedly married to Aylsie Elliot)
                         │   │   │   ├── Archibald Fairbairn
                         │   │   │   ├── Agnes Fairbairn
                         │   │   │   ├── James Fairbairn
                         │   │   │   ├── William Fairbairn
                         │   │   │   ├── John Fairbairn
                         │   │   │   └── David Fairbairn, b. 1822 m 1845 Charity Walker
                         │   │   ├── Thomas Fairbairn, b. 1794 (settled in Montreal)
                         │   │   ├── James Fairbairn, b. 1796 Kelso, Roxburghshire, SCT m. 1820 Janet Hunter
                         │   │   └── William Fairbairn, b. 1798 m. 1825 Isobel Synton,
                         │   ├── Walter Fairbairn, b. 1755 Smailholm, Roxburghshire, SCT
                         │   ├── William Fairbairn, b. 1756 Smailholm, Roxburghshire, SCT m. 1782 Margaret Thomson, b. Ednam, Roxburghshire, SCT  (schoolmaster Calashieldis)
                         │   ├── Andrew Fairbairn, b. 1758 Smailholm, Roxburghshire, SCT m. 1784 Margaret Henderson
                         │   │   ├── Sir William Fairbairn
                         │   │   └── Sir Peter Fairbairn
                         │   └── Peter Fairbairn, b. 1760 Smailholm, Roxburghshire, SCT (Barbadoes)
                         ├── Robert Fairbairn, b. 1716
                         ├── Thomas Fairbairn, b. 1718
                         ├── James B Fairbairn, b. 1720
                         ├── Isobel Fairbairn, b. 1722
                         ├── Hoge Fairbairn, b. 1724
                         ├── Agnes Fairbairn, b. 1726 m. 1747 Patrick Crawford
                         ├── Patrick Fairbairn, b. 1728
                         └── Margaret Fairbairn, b. 1729 m. 1751 James Hall

NB I am combining two separately provided sets of information received secondhand here, but both purporting to be from Reby's book and have not personally verified the excerpts are accurate transcriptions (Who's Which - LDS reference).
Documented here in order that it may be read in conjunction with the similar pedigrees here, and the DNA results to date (see also Hit or Myth?)

Comments in red from Reby, comments in teal mine

John Fairbairn  (fief of land from King James)
└── John Fairbairn  b. 1585 (live Graveston in Ednam)
       .
       .
    └── Robert Fairbairn b. 1662
        ├── Robert Fairbairn
        ├── Isobelle Fairbairn
        └── John Fairbairn, b. 1688
            ├── John Fairbairn b. 1714 Maherston Parish (Makerston assumed)
            │   + Lucy Eadster
            │   + Helen Anderson (of Rosburghshire)
            │    ├── William Fairbairn m. Elsie Elliot (schoolmaster) - schoolmaster William was of Bowden & marr. Margaret Scott, and uncle of Sir William, son of Andrew and Margaret (Henderson)
            │    │    ├──David Fairbairn (mill in Farrelton - also given as John, mill in Farrelton, same children, amongst others)
            │    │    │  ├── Archibald Fairbairn m Sarah Farrell
            │    │    │  └── William Fairbairn m Margaret Graham (William of Chelsea - NB the wives for Archibald and William should be the other way round)
            │    │    ├──Thomas Fairbairn M.D. m Helen Kinniburg (the Thomas marr. to Helen Kinniburg is the son of Thomas & Margaret (CLARKSON)
            │    │    └──William Fairbairn, b. 1790 Alderton/Yetholm, SCT d. 1867 m 1813 Jean Wanless
            │    ├── Andrew Fairbairn m. Margaret Henderson
            │    ├── Peter Fairbairn (went to West Indies, had large family, Secretary to Lord Seaforth)
            │    └── Walter Fairbairn
            ├── Robert Fairbairn
            └── Thomas Fairbairn b. 1718
            ├── James Fairbairn b. 1720
            ├── Isobel Fairbairn b. 1722
            ├── George Fairbairn b. 1724
            └── Agnes Fairbairn
 

And yet another version which adds wives to the earlier generations.
There was once a version of this freely available on the web, fully commented with sources and film numbers, can anyone find it again? I hadn't time to check the sources before it vanished (at least from my sight), and have not (yet) found references to all the wives' names mentioned (but haven't finished looking).  
The only remnant I can now find is on OneGreatFamily credited to a group named osullivan/cassidy, with no contact details available. Reproduced in full below apart from descendants of John and Jennett (JOHNSON) FAIRBAIRN, and some fuller date details of day/months

Jhone Fairbairne, b. 1563 Kelso
└──Jhone Fairbairn, b. 1585 d 1645 m 1611/2 Kelso Meg Porteous
     └──Robert Fairbairn, b. abt 1604 Kelso m Jul 1626 Innerwick, ELN Agnes Home
          └── Johne Fairbairne, b. 1637 m 1652 Greenlaw Issobell Purvis
               ├── John Fairbairne b. 1658 Stitchel, ROX
               └── Robert Fairbairne, b. 1662 d 1697
               m1  
                 └── Robert Fairbairne
               m2 Marion Haitlie
                  ├── Isobel Fairbairne
                  └── John Fairbairn, b. 1688  m. Magdalen Bo
                       ├── James Fairbairn, b. 1720 d Oct 1808 m Nov 1754 Legerwood Elizabeth Purves
                       │    └── John Fairbairn, b.abt 1772 d Jul 1824 m Jennett Johnston (with further details on this line only)
                       ├── John Fairbairn m Helen Anderson (compare with BO pedigree  - F-17/F-38 results) 
                       ├── Robert Fairbairn
                       ├── Thomas Fairbairn 
                       ├── Isobel Fairbairn
                       ├── George Fairbairn
                       ├── Agnes Fairbairn
                       ├── Patrick Fairbairnm Margaret Purves
                       └── Margaret Fairbairn m J Hall