Weight can matter depending on how your hunting. Most of my rifle hunting is from a stand for deer. Other than carrying the rifle in and out of the bush, coupled with the fact that there isn't a lot of shooting, weight really isn't that much of a factor. Rabbit hunting behind dogs, where your walking all day and kicking brush piles, is where I really like a light weight shotgun. The big browning A5's really start to get heavy about 3 in the afternoon and is much better suited in a duck blind. Same thing quail hunting.....lighter and shorter is better especially when the cover's thick and on the days the birds are hard to find. Every hour that passes, the guns get heavier......
I've also found, by struggling through the briars and thickets, that barrel length means alot in this situation. When things are tight, just a few inches can save a lot of effort. Chasing down the dogs when their running "off" game is where weight and barrel length can be a real burden.
IMHO barrel length and weight are much more important on a shotgun than on a rifle, but it all really depends on how you hunt.