My personal opinion.
A true "lightweight mountain rifle" should be under 8lbs scoped and fully ready to hunt. It should be chambered in a round capable of taking the game it is intended for out to 700-800 max. Deer/sheep something like a .260 Rem, for elk/bear, maybe .280AI, etc. Less recoil helps with making it a bit more forgiving on non-prone field position shots. Not that the rifle is any less accurate than a 15# rifle, just that it takes much more consistent shooter input and recoil management to maintain the rifle's ability to shoot to it's full potential. I do not have any sub-8# rifles myself, but I have shot plenty of them. Good example is a 7lb 1oz .300WM I have shot on numerous occasions. Prone with a good rest, I can shoot sub-1" groups at 200 yards, and hold half MOA out to 600. But off a bench, sitting, etc., accuracy that I can hold goes down. It is a great mountain elk rifle though.
A "longer range carry weight" hunting rifle should weigh between 9-12#. I have carried heavier, but not a lot of fun. You can step up in cartridge capacity with this weight. For deer/sheep/elk, you can easily go up to a magnum cartridge. 6.5 SS, 7RM, .300WM, 28 Nosler, etc. and still shoot very accurately. I have 4 rifles in this weight range. 6CM, 6.5SS, .280AI, 7RM. My .280AI actually weighs 8lb 13oz, but close enough. All of there rifles can shoot under 3" out to 900+ with good conditions.
A true "long range" rifle, again in my opinion, needs to step up again in case capacity and bullet diameter/weight. Long range to me is 800-1200+. Personally, I shoot steel and coyotes as far as I can see them. But I would never shoot at big game over 1200. Probably over 1000 actually. Something like .300WM, 28 Nosler, .300RUM, .300NM, .338 RUM/Edge, etc. pushing heavy for caliber bullets. 7mm 180-197, .308 200-230+, .338 250-300.
Rifle weight on my personal long range rifles are 15#+. I have two in this range. One for elk, one more for coyotes/antelope/maybe up to deer out to 1000, and a lot of 1000-1500+ practice time on steel. A .300RUM pushing a 230 Hybrid @ 3068fps, and a 6.5SLR pushing a 140 HVLD @ 2930. The heavy rifles are much easier to shoot well.