Average run of the mill 20" Marlin 336's weigh in around 7lbs, Winchester and their clones weigh in less, pistol caliber carbines less, 16" trapper types less. As a matter of fact it's a lot easier finding 8lbs bolt guns than 8lbs lever guns.
I'm not sure what the weight savings will be changing out stocks. Guns can be as much about balance as weight. And a few ounces here or there can definitely change the feel of a gun. Personally I feel weight of a gun can be very misleading and I've seen heavier guns that carry and feel lighter than other, lighter guns. Take the lever vs. bolt gun. Even in comparable weights the lever guns carries better and within the realm of .30-30 lever guns, the Win 94 has a completely different feel than the chunkier 336 despite only a few ounces weight difference. But it's just dang hard to get one gun, regardless of platform, lighter than the next. They all need stocks, receivers, bolts and barrels of a minimum thickness. All the OP can do is change the stocks and see what happens.