Facts we can divulge from the song:
1) The story takes place in Mississippi. Choctaw Ridge, Carroll County, Tupelo, and the Tallahatchie Bridge all exist in real life. The opening line suggests the speaker lives in the Delta religion of the state, which is located in nothern Mississippi.
2) the speaker's father does not care much for Billy Joe, her mother is more sympathetic, and her brother was apparently a friend of his at one time.
3) the speaker apparently had some degree of sympathetic relationship with Billy Joe. She was talking to him at church and was seen with him on the bridge. When she finds out he is dead she loses her appetite (unlike the rest of the family) and later spends "a lot of time" throwing flowers off the bridge in what is clearly some sort of memorial tribute.
4) the family of the speaker is largely oblivious to the relationship she had with Billy Joe, and for some reason she has no interest in bringing it up.
Unresolved questions from the song:
1) What did the speaker and Billy Joe throw off the bridge, and at what time did this event occur? The fact that Brother Taylor visited the speaker's house on the same day Billy Joe died does not necessarily mean he saw the girl and Billy Joe throwing the thing off the bridge on this day as well.
2) What degree of relationship did the speaker and Billy Joe have? Was it sexual? Ages are not given, but it is suggested that the speaker is at the very least a teenager. She lives with her parents, but is capable of doing hard labor in the field. Her brother is old enough to get married and move out of the house. The brother recalls putting a frog down his sister's dress- a rather immature stunt- but this likely happened years ago and is being remembered out of nostalgia.
3) The key question- why did Billy Joe commit suicide, and to what degree was this related to:
-his relationship with the speaker
-talking to the speaker at church the Sunday prior
-he and the speaker throwing something off the bridge
-visiting the sawmill the day before
Themes
Regardless of the unanswered questions of the song's plot, the song nevertheless contains several themes. The first is simply that of a "period piece" of Southern life in the early 20th Century.
The other theme is a darker one, about the indifference we often show towards the loss of human life. The speaker's family talks about a young man's suicide in the most nonchalant way possible. The line "Well, Billy Joe never had a lick of sense/ pass the biscuits, please" is a great example. Aside from the speaker, no one seems to know or care much about Billy Joe. His death is just a source of dinnertime gossip, like the weather.
Theories
1) The most common theory is that Billy Joe and the speaker were indeed involved in some degree of romantic / sexual relationship that was kept hidden from the speaker's family because the father strongly disliked Billy Joe. This in turn is commonly interpreted as meaning the couple had an unplanned child at some point, and they threw the baby off the bridge together rather than deal with this manifestation of their illicit relationship. The guilt stemming from the murder of his own child later in turn caused Billy Joe to kill himself.
Some have gone even further and speculated that because the child was unwanted, it was either stillborn or aborted in some haphazard fashion, and then quietly "disposed" of off the bridge to hide the proof that the pregnancy had ever occurred. I've heard some point to the relevance of the "Child, what's happened to your appetite" line as a subtle key to this. Loss of appetite commonly occurs after giving birth. But it also commonly occurs when someone is depressed.
2) Another theory is that Billy Joe and the speaker are different races. This is consistent with the song's Southern theme and may explain the speaker's motivation for keeping her relationship with Billy Joe hidden. The food being eaten at dinner may be intended to represent traditional black Southern cuisine, and the mother's use of the word "child" to address her daughter is a rather distinctly African-American expression. The speaker similarly mentions picking cotton, which is likewise a chore that has been primarily associated with Southern blacks since the days of slavery. An inter-racial relationship during the period in which the song is set would clearly be a social taboo, and may have led the speaker to break up with Billy Joe, who proceeded to commit suicide. The unwanted child theory can be similarly strengthened by this premise, as a mixed-race baby would be even more socially unacceptable than an mixed race romance.
3) A third theory says that Billy Joe's suicidal tendencies were well-known to the speaker. The thing thrown off the bridge was thus a gun, after she successfully convinced Billy Joe not to kill himself. But then later he jumped off the bridge anyway, proving the failure of her efforts.
