Fayette Co. marriage records list John Petitt m. Nancy Berry, 2 May 1811.
Fayette Co., Will Book D, p. 158, 1816, records an estate inventory for John Petit, no heirs named. Kentucky Gazette of 12 Nov 1819 posts a notice by Geo. Berry, administrator of the estate of John Pettit, dec'd, who lived 8 miles from Lexington on Hickman road, regarding a runaway slave named Bazil. (The notice mentions James McCleary and William T. Bryant.) Since this sounds like the address of the home of Nathaniel Pettit, Sr., since John married a Berry, and since no other John Pettit is listed in the 1810 census of Fayette Co., I conclude that the John Pettit who died 1816 is the son of Nathaniel Pettit.
Census
1810 census of Fayette Co., Ky, p. 25, lists family of:
John Pettit, 1 m 10-16, 2 m 16-25, 1 f < 10, 1 f 26-45.
(This household consists of the children of Nathaniel Pettit Sr., who died in late 1809, and whose estate was divided in 1814 between 3 sons and 3 daughters. However, at least 2 of those daughters had married before 1810, the other is likely to be the girl under 10, and John did not marry until 1811, so I am not sure who the older female is. Perhaps his mother??? It may be that she was still alive even though not listed in Nathaniel Sr.'s estate settlement.)
Notes for Nancy Berry
There is no Nancy Pettit in the statewide index to the 1820 census of Kentucky. She may have remarried by then, but on the other hand, she is probably the Nancy Pettit in the 1830 census reading below, so most likely she was living with a relative.
1830 census of Fayette Co., Ky, lists on p. 358, 6 lines down from the Harry Pettit family:
Nancy Pettit, 1 m 10-14, 1 f 30-39. This is probably John Pettit's widow. I have not identified any other male Pettit in Fayette Co. who could have died in the period 1816-1830, and she is living near John's brother Harry. Nancy and John's son William was 18 in 1830, so the m 10-14 is apparently another son. Since John died in 1816, this son must be at the high end of the age range.