I have been looking far and wide around my property here in NC for a decent size osage tree. I have found a few small ones not big enough for a bow. However, I just stumbled across what I thought (at first) was a group of good ones! Only one problem. The leaves have small serrations along the edges.     Here are some pics I took for some help. Tell me what you guys think. Thanks!
  Possible Osage

That is an escaped Bradford pear. The wood is strong and should make a good bow...but it isn't osage. The ball you have in the pic looks like an old sycamore ball.

...also, most osage 2" or bigger will make a hunting weight bow. I've made a few very good osage bows from 2" diameter shoots, sapwood and hardwood were used in these bows.

Thank you. Well I have found a few that are about 5 inches or so at the ground but they taper very quickly. The woods here are very thick and therefore these trees are forced to grow straight(of-course not actually straight   ) up and not out at all.  Giving them little girth.  I will give one a try though!!  Thanks again!

5 inch diameter is plenty.  A little crown in the back of the bow won't bother performance much. My best bows have come from 6 to 12 inch trees

Thank you