I've owned and used several NULA's, and the stocks can vary as much in weight as #1 and #2 contour barrels--not much, but some.
As for balance, it depends on the shooter. The first NULA (actually ULA) I owned was a Model 24 .270 Winchester that my wife hunted with for a number of years. It had a #1 22" barrel and weighed 6 pounds exactly with a 2-7x Bausch & Lomb scope. Eileen killed two deer offhand with it at 150-160 yards. She doesn't like rifles to be much heavier, because she can't hold heavier rifles offhand as steadily as she can light rifles, no doubt a question of upper-body strength as compared to the average man. That rifle also grouped three shots in about 2" at 300 yards with the load we settled on, using IMR4350 and the 130-grain Nosler Partition.
For a while I hunted with a Model 20 in 7x57 with a #1 22" barrel, and had no difficulty killing animals offhand at typical "woods" ranges--though I never shot any at 150 yards. It weighed around 5-3/4 pounds with scope.
For over 20 years have hunted with a Model 24 .30-06 with a 24" #2 contour that weighs 6 pounds on the nose with a 6x33 Leupold. Have shot a few animals offhand at close range with it too, but also a few at 400+ from prone. Probably could have done the same with a #1 contour but who knows?
