In fairness, when I say “6-7lb rifle” meaning a bare rifle, but the “11lb rifle” I take up mountain each year is a rifle and scope, 11lbs as hunted.
Regardless of chambering, instability on target is instability. Movement in recoil is movement in recoil. Recoil tolerance isn’t part of my equation.
I don’t pack only the most minimal weight possible, so I don’t prioritize minimizing my rifle weight. I can cut 2lbs out of my load by using a lighter frame “hunting” model pack (nearly identical pack), but I like the “tactical”frame better than the Hunting version. I can cut about 4lbs out of my daypack by reducing my water carry, and can cut a pound out by eliminating my emergency water purification pump and overnight camp. I can cut a pound and a half of weight out by eliminating my koolaid powder mix I like to have with supper each evening, and another pound by eliminating Oreos and Snickers which I take for after supper comfort food planned for 3 out of 10-12 nights. I can cut a pound out of my pack by using a lighter tripod, rather than the carbon fiber pod I use which can support my rifle and is more steady than my lighter tripods. I can cut a pound and a half by carrying my G20 10mm instead of my Ruger Toklat 454C. I carry about 50% more daily food than I need. The only weight savings omission I have made in many years is to stop taking a spotting scope, in favor spotting with binos. I can cut a pound out by leaving my Satellite communicator at home - a relatively new device I lived without for many years, but appreciate having available now. I could reduce my body mass by about 8lbs as well, which typically offers a doubling effect to make my pack feel lighter and more manageable as well... I’d cut any one of those extra weight choices long before I made effort to cut ~3-4lbs off of my rifle. I know I could scrub a pound and a half off of my rifle as it is today, but after changing the stock 4 years ago, I simply have not been motivated to do so...
...because the rifle weight is worth it to me when the time comes.