Local chap bought one of the Remington Stainless 700's with a laminate stock and pencil weight barrel. It wouldn't shoot his old favourite load that worked so well in his 1600 Husky - best was 2 1/2" at 100 meters.

I pulled the barrelled action, relieved the 60 or 70 pounds of forend tip pressure that was bending the barrel, then had to re-bed to get the action aligned and square in the barrel channel. I put in 1/2" of bedding under the barrel shank, the rest floated. I think I only used JB Weld Epoxy for that job. East to use and synthetic axle grease for release agent.

With Federal 165gr. Fusion, it shot 1/2 to .6", and with Federal 165TSX factory ammo, it ran 3/8" to .45".
It still wouldn't shoot the 180's any better than before. LOL.

Shad shot, elk, moose, whitetail buck and a stone ram that fall, all with the 165gr. Barnes factory Federal load and all with one shot each. All but the elk were close, less than 150yards. The elk was 415yards, iirc.

So, I guess the point of all of this is, some light weight rifles will shoot.