I've found light rifles will work quite well if you practice with them. There's also some virtue in having a heavier, longer barrel on a light rifle, but the balance and weight also depend on the shooter.
My wife has killed two deer offhand at 150 yards quite neatly with a NULA .270 weighing 6 pounds on the nose with scope, and remarked that the rifle didn't wobble nearly as much as heavier rifles that were harder for her to hold up. I've killed several animals at 350-450 yards with a NULA .30-06 weighing not much more, using field positions ranging from sitting with the rifle over sticks to prone with the rifle over a daypack. Haven't tried shooting anything beyond 450 with that rifle, but then I don't usually shoot beyond 450 at big game with any rifle.
In discussion like this somebody always comments on how shooters fixated on rifle weight would be better off losing some weight themselves. No doubt that's true, but at a certain point it's irrelevant. I've found that when hunting and packing out game on foot, less weight ANYWHERE is advantageous, especially as I get older, whether the weight comes off of me, my rifle, my boots or my pack.
