There is a lot of misinformation on this subject.
My hill stalking rifle is a 7Lb (scoped) 7mm08. It's home loaded and shoots 1/2" providing you don't heat it up too much. #4 profile fluted barrel. It's actually a bog standard factory Remington 700 Ti with Talley mounts and a Swaro Z3 that has been properly bedded.
It's a great rifle to carry and does all I need it to do at stalking ranges. In January on the hinds it was good for two 5 hinds sittings - 5 for a group in under a minute - no loss of accuracy but I probably wouldn't want to take any longer shot strings with it. Furthest shot was a sika calf who ran when I shot the hind. It was shot when it stopped at 360 meters. I really don't need anything heavier for the hill and certainly don't for woodland stalking where I have not taken a shot longer than 100 meters all year. The comb isn't quite high enough but that is taken care of with a removable cheek raiser/bullet pouch which get's me to the right height and means I carry 5 spare rounds on the rifle at all times. When the average day out is a 15km walk with 1000m of ascent why on earth would I want to carry anything heavier?
I wouldn't choose that rifle for any long range work over about 400 meters. For that I have a 14 Lb 6.5x47 lapua with a heavy barrel and big heavy scope on it. It is a more stable platform, it has an adjustable comb, recoil is negligible and I never fail to see shot strikes. It's a better tool for that job, but that job is not stalking and I rarely have to carry it too far.
To write off all rifles that are not tacticool and weigh less than 12Lbs is madness and shows a very poor understanding of stalking.