Ya, lbs is actual weight. Carry a 10 lb bow and your carry weight goes up 10 lbs. Damage is probably the closest in-game comparable to draw weight. I don't know real bows though, so I don't know that you necessarily expect a harder hit from a bow with a harder draw.

Draw speed varies. The higher the number, the faster the draw, the quicker you can get an arrow off.

Damage is damage. But the higher damage bows shoot flatter than lower damage ones. That said, I can't tell the functional difference (on a console) between any bows except between the long bow and all others. Long bow, I need to aim high for distant objects. All others are functionally flat shooting for anything bigger than a rabbit at 500 yards.

Weight is how much the bow weighs when you pick it up of the ground. Its only concern to the player is how much stamina am I going to use while sprinting if I have this bow equipped.

I forgot to add that I love to use a crossbow with my mage so he can use Weakness to magic poison and then swap to using destruction magic on his foes

This is very true. I don't even play with Daedric armor or anything with Dragonbone on most of my characters. I just pick the stuff they look the coolest with or most fitted with and play them like a boss! Heck, if a bandit maurder can slice through dragonbone like butter, then so can we! Hail the forsworn!