Probably none, and it my well weigh more. I've weighed a lot of stocks and have found that most of the inexpensive plastic stocks weigh more than comparable wood. The only synthetics that offer any weight savings are the $600 customs made by McMillan and the other high end custom stock makers.
If you want a 7 lb scoped rifle you need to be looking at bolt rifles. Lever guns are just too heavy. About the lightest are just under 7 lbs up to 8 lbs before adding glass. There are plenty of bolt rifles from 5 lbs up to just over 6 lbs that could easily be kept under 7 lbs scoped. And many cost less than a lever action.
These are photos of one of my 870's in both a factroy plastic stock and factory walnut. The plastic stock is 1/4 lb heavier.