That crossed my mind too Nigel. But the lassie was 'out chopping cotton', which would perhaps be rather exhausting if she'd just given birth/had an abortion.

They say that Bobby Gentry has been asked about the reason for the suicide of Billy Joe, and she didn't have any answer. She said she wrote the song off the top of her head and couldn't give us the story behind it.
I do like to get to the bottom of things. Very frustrating not to know!