I have read, that if you double the width of the bow, you double the weight. If you double the thickness of the bow, you actually increase the bowweight by a factor of 8.
This translated is, that a very little wood removed from the belly goes a long way in reducing the weight of the bow, where if removed from the sides it would actually not matter so much.
I am a bit tired right now, and I am not sure this is correct, but I think that if you were to remove 1/8 of the material from the belly, you would actually half the weight of the bow?