Ive made bow or 2 from a very thin stave, usually the B side from sawing a log in half.
One was very thin in the handle, barely an inch. I just reduced the stave to a good thickness taper and didn't aim for a weight.
So, if you have a thin spot to begin with, reduce the whole bow so its no longer a thin spot. I won't even think about bending a
bow until the thickness taper is as perfect as I can get.