I've put leather sweat bands in a couple hats for myself using a backstitch. I used about a 2/3 oz leather. The bad news is, after sweating and getting the band wet, when it dries, sometimes it shrinks so much, you can't get the hat on. Since your hats are heavier, you may not have that problem. If I were to try it again, I would try to check out some hat suppliers websites to see if sweat bands are made of a specially treated type of leather.
Good luck,
Kevin