Draw weight doesn't depend on the size of the bow. The bowyer decides the draw weight when he makes the bow, and it doesn't matter whether it's a shortbow or a longbow. But the longbow is usually smoother to draw than the shortbow, because the bow limbs bend more on a shortbow, which can cause staggering. Also I know people who shoot with 100 Ib longbows, and they don't draw any slower than people shooting lighter shortbows (although they get fatigued more quickly).
This.
Short bows are made for hunting because they are easier to handle and attracts less attention, but the draw strength can be way higher than a long bow. It all depends on the bowyer and which purpose the bow was made for. As far as I'm concerned it would be nice with some variety in bows, but it shouldn't affect the stats. Only material and quality of craftmanship should. And different types of arrows perhaps, although most all arrows would probably be broad heads as you want to kill what you shoot at in this world.
A variety in bow sizes and draw strength would also prompt a need for different arrow lengths and shaft types IRL, but that would be too complicated for a game.