When I went to my WORKING file, I DID find the surname Weldon. It seems that Ann "Nancy" Pitts, daughter of Hardy Pitts who died 1784 and his wife also named Ann "Nancy" Williams who lived 1748 to 1830. The daughter died in Halifax co., NC in 1842 or 43. Her children by Weldon ( I have no other names or dates) are: Hardy, Mary Polly, Daniel and Matthew.
The elder "Nancy" seems to have been daughter of Capt. Nicholas Kinchen Williams and possible wife Ann Roper or Roaper.The elder "Nancy" has a will that says following:
Her Will: Grandson Thomas Parham; sons Walter and John Pitts; daughters Nancy Weldon, Martha Harrison, Silva Lane. Exrs. sons Walter and John Pitts. Wit: J. Nicholson, P P Harvey. Dated Feb 3 1830; Probated May 1830 (Anderson: Abstracts of Wils, Halifax County North Carolina 1760-1830 p. 65.
Her parents were: Capt. Nicholas Hunter Williams and Ann Lewis... and Nicholas was a son of John Williams whose wife is controversial... but I believe is Anne Whitley.
I don't know anything more and that is the only reference I have in my file.