I have just started to analyze the 1900 census entries, and here is what I tentatively know about those Williams:
Robertson Co TN (the faded and smeared one) I think that is John Gamble Rigsby, son of Sidney Rigsby. Sidney was from Sumner Co TN. He married Eliza Griffin, but may have had an earlier wife who was John's mother.
Sumner Co TN (Thomas + Alice) Thomas was son of Ausburn Rigsby + Mary Lain. Ausburn was a brother of the above Sidney, they being sons of James Rigsby who was son of Luke.
DeKalb Co TN (the step-grand-nephew of T Fite?) I looked at the entry again, and now I think the name is Filts, instead of Fite. That's still just a guess, though. This one will be hard to track down. It looks like Hattie married a Rigsby about 1891, they had a couple of kids, and then he died before 1900. Which Rigsby she married is hard to say. All the DeKalb Co Rigsbys were from Canada, son of Thomas. So far I don't know of any of them marrying a Hattie or Harriet, but I haven't looked at all the records for DeKalb Co.
I don't know anything about those families after 1900, but maybe someone else who does can tell you about the William in each of them. Of course, you will probably end up being from the one in DeKalb, since he will be the hardest to trace.