The name "Benjamin G.E.O. Pettit" is from a family group for David Sook on p.72, Zug/Zuck/Zouck/Zook Genealogy, by Harry D. Zook. I can't help wondering if this is a misinterpretation of some record and it really represents a middle name of George, though. He doesn't say where he got the "G.E.O." from; the marriage record gives no middle name or initials, and I haven't found a census record for this family. I doubt it is from probate or cemetery records, as the Zook book gave no date or place of death. Perhaps land records? Mr. Zook seems to have examined a lot of them.

Marriage records of Franklin Co., KY, list marriage of Benj. Pettitt and Kitty Zook, 22 June 1826.

1820 Census of Franklin Co., Ky, lists on p. 112 an entry that could be Benj. Pettit. But it is indexed as Benj. Penn, which it could also be. Or even Perrin or Penin. This census page is so faint that the tops of all the lowercase letters are invisible, and the handwriting is such that the bottoms of many letters are indistinguishable. The name has 5 "waves" after the e, which seems one too many for Penn. (There is no Benjamin Pettit or Penn or any similar name in the 1810 or 1830 censuses of Franklin Co., so that isn't much help.) I also cannot really tell which columns are marked. It seems to be in the sixth and seventh columns, which would be 1 m > 45 and 1 f < 10, but that doesn't seem like a very probable combination, so I may be misreading it. Maybe I'm one column off, and it's really 1 m 26-45 and 1 m > 45. If so, the younger one could be this Benjamin, still unmarried, and the older one could be his father (as well as maybe the father of the other Franklin and Henry Co. Pettits??).

I cannot find this family in 1830 or later censuses (and there are statewide indexes through 1840.) They may have moved out of Kentucky. Or perhaps Benjamin died, and Kitty had either already remarried by 1830 or was living with her parents, so that she was not a head of household.