I agree with Anne, for normal bichirs you don't want them to be much thicker than their heads. Once you start to see a bulge just behind the skull, it's time to cut back on feeding.
Just as with most animals, it's not healthy to eat too much.
Elindra, I consider SB a separate case. Because their physiology is 'smushed' it is actually normal for them to look obese, when that is actually their normal shape.