The way the census record is laid out suggests to me that Willie might be Hattie's son.
The record starts with the Head, his spouse and their children (all normal), it continues across the page with two more children and then a servant (all normal so far), then there is another "son" then a sexton.
The "son" coming after a servant makes sense, if he was a son he should be listed with the other children. What I have seen in other census records is that in complex households (such as multi-generation families) the children of other adults are listed as related to the Head when really the relation is compared to the previous adult in the record. I've also seen where a daughter-in-law is listed as "wife" because she is the record following the Head's son.
Now the issue with this theory is that Hattie is listed as aged 18 initially then changed to 17 while Willie is 9, I don't think this is biologically possible?
The "sexton", Sidney, is also an oddity. His occupation is listed as sexton but why this is also recorded as his relationship to the Head I have no idea. If Hattie and Willie are siblings then Sidney could be an older brother, alternatively if Hattie is Willie's mother could Sidney be his father?
Alex Moes, I agree with everything you said. Sidney is listed as a sexton, because the head of the household was a preacher and a sexton is the caretaker of a church, so I presume that's why. I think Sidney, Hattie and Willie are probably siblings.
Since Willie wasn't employed by the head of the household, maybe "son" was just used in a generic sense of the word.
My grandmother and my mom and aunt are listed as boarders in the household of my great-grandparents, not as daughter and grandchildren. Possibly because my grandmother was working and paying room and board, but that's just a guess as to why it's listed that way.