A scoped 6.5x55 lightweight modern boltgun, beit a Winchester M70 FeatherWeight, or Tikka - or whatever.
Any of which should come in weighing 2/3 that of most AR's, except a Carbon 15 (5lb) or a pencil-barrel lightweight special build.
My M70 FW in 6.5 Swede weighed in at 7#, with a Leupy Compact 2-7x, with not as much recoil as any of my .30-06's.
I've found I like a light rifle, since they're carried more than shot.
The exception, IMO, would be that a heavier rifle better as a stand/beanfield sniping rifle.