What did he and the girl throw off the Tallahatchie Bridge?
Apart from himself? 
I always thought it was her baby (illegitate and all), but I can’t remember why, so I’ll search. I guess I thought Billy Joe killed himself out of guilt…
No one knows (including the song’s author).
It was irrelevant to Bobbie Gentry’s point in the song.
(There is, of course, wild speculation, furthered by the rather silly TV movie that was made based on the song’s popularity, but there is no real “thing” that was tossed.)
Among references (on the SDMB):
Original Ode to Billie Joe lyrics?
And some odd speculation from the 'net:
So what did Billie Joe MacAllister throw off the Tallahatchie Bridge?
The song definitely avoids telling us what, specifically, they threw off of the bridge, and the few articles I have read about Bobbie Gentry have always maintained that she never publicly stated what she meant by that part of the song as well, so I don’t believe we’ll ever know. There was a movie based on that song if I am not mistaken, but the what they threw off the bridge in the movie is not mentioned in the song.
The throwing off implies some significant point in the relationship. The text of the song as a whole makes it pretty clear that the sister was the girl there, and the incident meant something to her. It’s natural to wonder what was thrown off, but naming an object wouldn’t really add to the story, and would likely distract one from the point.
In the movie, of course, such artistic subtlety would be too demanding for the expected audience, so they created a doll-cum-imaginary friend (“Benjamin”) that got thrown off. It seemed to signify a rite of passage in the girl’s growing up.
Since this is about a song, I’ll move this thread to Cafe Society.
bibliophage
moderator GQ
I’ve always thought it was a newborn baby, and Billy Joe later killed himself out of guilt. A haunting song, regardless.
Just out of curiosity and meaning no disrespect to the OP, but how many more times does this question need to be posed before it joins the hallowed ranks of “words that end in -gry,” “where did the last dollar go” and “does a duck’s quack echo” that get mocked openly and viciously every time it’s asked? 'Cause I wouldn’t want to be late to that party.
I think that doing a search in this forum, using the song title, will bring up at least three threads that discuss this topic extensively.
My 'puter is acting very slow and lazy tonight, so I won’t try to search and link.