I have been watching this ultralight mountain rifle debate for 30 years, and it is amazing as to what lengths guys will go to in order to shave mere ounces from their rigs.
Seen rifles down to the 4lb range range (remember the Kifaru?).
One of the most common results is that people find how hard it is to steady an ultralight rifle in order to make that shot on a ram at the end of the climb when they are breathing hard and their heart rate is up. Most of the guys I know personally ended up selling those early ultralights and building another rifle with a little more weight, ending up with scoped rigs closer to the 7 lb +/- range as indicated by the OP. Made the rifle more shooter friendly, under all circumstances.
Personally, the rifle I carry in the mountains most is a custom lh Sako AV in 7mm STW with a 24" barrel in a Fajen laminated stock that weighs 7lbs bare. It's Leupold VX III 4.5-14x40 B&C is in steel Leupold rings. Never have weighed the scoped rifle with shells in it, but it has served me well and never felt overweight. It has accounted for sheep, mountain goat, elk, deer and moose over the past 20 years, and been on many more climbs for sheep and goats than any other rifle I own.
The biggest factor, I believe, is how it handles and balances; a slightly heavier rifle that balances well and handles easily is a joy to use, and may not feel as heavy as the scale indicates.
Other weight savings or trimmings can come from your other gear you are using/packing to lighten your overall load. Then there is your own weight.
If I dropped another ten pounds, I can carry an extra pound quite handily! LOL