I've a family group sheet that was shared with me some years back, so this is not all from my own research.
Partially from Fayette Co., GA. census 1810 and Campbell Co., GA. census 1860:
Bartlett J. Walker; b. 1816 married 9 April 1837 in Fayette Co., GA. wife: Mary Abercrombie; b. 1814 in Laurens Co., S.C. father: William Abercrombie (c.1769-1855) mother: Sarah A. Picard - not sure, but very likely.
Sarah A. Picard; b. abt. 1772; d. abt. 1816/17 SC m. abt. 1789 Laurens Co., S.C. Mary Adams; b. 1779; d. 1860 Fayette Co., GA. m. abt. 1818 possibly in Laurens Co., S.C.
Children born to Bartlett & Mary (Abercrombie) Walker:
1) Bartlett; b. 1843 2) Hardy; b. 1844 3) John Pearce; b. 14 June 1846 Campbell Co., GA. married: 6 Feb. 1868 died: 20 Oct. 1927 Hightower, Cleburne Co., AL. buried: Ranburne Cemetery wife:1st. Nancy Elizabeth Fowler; b. ?; d. 1908 Note: Shows he served CSA 4th GA, Inf. 4) James; b. 1850 5) David; b. 1853 6) Mary; b. 1855
There is also an even more complete family group sheet on John Pearce Walker and his wives and children if interested.
William Abercrombie; (c.1769-1855) d. Fayette Co., GA. It is unclear to me just how many children were born to him.Names as I have them: 1) John; b. abt. 1791; d. ? m. date? wife: Elizabeth [--?--] 2) Thomas Jackson; b. abt. 1794; d. 1854 m. abt. 1820/21; wife: Rhoda Rose 3) unknown 4) Hanna; b. 1802; d. 1890 m. date ?; husband: James Baxter 5) William; b. 17 July 1804; d. 10 July 1885 m. 13 July 1826; wife: Sephronia Ashman 6) James B.; b. 1807; d. ? m. date?; wife: Sarah A. Thomason 7) Elizabeth; b. 1809; d. ? m. 11 Jan. 1827; husband: Rural Edwards 8) Issac; b. 23 Oct. 1811; d. 23 Sept. 1855 m. 2 Nov. 1837; wife: Nancy Jane Dowdy 9) Mary; b. 1814; d. ? m. 9 Apr. 1837; husband: Bartlett J. Walker 10) Sarah Aracey; b. 12 June 1819; d. 12 Nov. 1896 m. 5 July 1840; husband: Dick Clark Camp 11) Henry David; b. 1820; d. 14 Dec. 1863 m. 22 Dec. 1839; wife: Lucinda Wells
All but the last two of the children were born in Laurens Co., S.C.The youngest two were born in Georgia. Henry David being born in Campbell Co., GA.
Looking at one of my notes, I'm inclined to think that your Mary (Abercrombie) Walker was a daughter of William and his 1st wife, Sarah Aracey Picard. It appears to me that she died between 1816 and 1817, and that William married Mary Adams about 1818 possibly there in Laurens Co., S.C.
William Abercrombie (c.1769-1855) father: John Abercrombie; (c.1736-1816) mother: Ann Kellett; (c. 1742 - ?) dau. of Josheph & Jenett/Jane Joseph & Jane were residents of Laurens Co., S.C. and both of their wills were made in Laurens Co., S.C.
Best information I've found indicates that John Abercrombie (1736-1816) parents were: father: James Abercrombie; (c.1708-1782) mother: Hanna Pickard (c.1798- ? )
If I may be of any further help, please contact me firstname.lastname@example.org