You can take quite a bit of weight off and still be safe. But the lighter you go, the more difficult they are to shoot off-hand.

I have a 7 x 57 on large ring, standard length action that weighs 5# 7 oz. It has a shaved down 1909 steel trigger guard and a Leupold 4X Compact scope in skeletonized steel rings, with back-up steel open sights. It has a very trim 21" barrel and a minimal "toothpick" Old World walnut stock. The only aluminum parts on the rifle are the Timney trigger housing and the replacement alloy follower.

It is wonderful to carry, but difficult to hold steady.

One would probably be better off starting with a lighter weight action (Rem. M600-700), but I have little interest in bolt rifles that are not Mausers.