I found a non-population schedule in Clays, Washington, Georgia with Benjamin Hood listed in the same schedule with a lot of other Hoods.
in the U.S., Selected Federal Census Non-Population Schedules, 1850-1880
Perhaps this record has more data?
in the Georgia, Compiled Marriages, 1754-1850
I think I found him in the 1860 census. This one says he was born in South Carolina, which could offer another clue to his birth.
"United States Census, 1860", database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MZMT-YW1 : 13 December 2017), Benjamin Hood in entry for Susan Hood, 1860.