William was born in 1850. He was either the son or grandson of Maria Williams.
The 1880 census lists Maria as the grandmother of the head of the household. She would be just old enough to be William's grandmother, but age also fits well for her being William's mother. And because William had several children by 1880, it is entirely possible that he'd gotten into the habit of referring to Maria as "grandmother" for the sake of the children.
W > Williams > William Williams
Categories: US Black Heritage Project, Needs Sources | 1880 US Census, Franklin County, Georgia