Bombur is the fattest of the dwarves. No, really, that's his character trait. He's always huffing and puffing and falling behind simply because he is quite large. This proves to be a real problem when the dwarves are in Mirkwood. A deer suddenly comes out of nowhere and knocks Bombur into a forest stream. The water is enchanted, and thus Bombur becomes incredibly sleepy and inclined to dream about fine elvish feasts. So the rest of the dwarves have to carry incredibly heavy Bombur all the way through the forest. This only makes them more irritable and inclined to go off the path into the forest (against the advice of both Gandalf and Beorn).
Bombur's fondness for sleep also contributes to Bilbo's plan to sneak out of the Lonely Mountain and hand the Arkenstone of Thrain to Bard. Bombur is on guard the night that Bilbo leaves his friends. He tells Bombur he can't sleep, and offers to stand watch instead of Bombur. Bombur agrees readily, and Bilbo uses this time to visit Bard. So if Bombur were a little more alert and less willing to grab a nap whenever he possibly can, Bilbo would never have been able to take the Arkenstone out of the dwarves' camp. Bombur seems like a decent guy and, frankly, we agree with him in preferring a good nap and lots of food over, say, war and danger.