My current gun with scope weighs about 8 1/4 lbs. My scope weighs more than I'd prefer but I like the 3-18x option for long range shooting. 7mm RM.
Fiftydriver is building me a rifle now in 300 WM and my goal was to keep the bare rifle's weight down to about 7 1/2 lbs max. He's putting a #3 contour Lilja barrel on a Lawton 7000 action.
I carried a 338-378 single shot rifle up goat hunting once when I was younger. The rifle alone weighed about 10 1/2 pounds. Probably 12 -12 1/2 lbs with the scope and sling. I shot a goat from about 225 yds. More or less blew him off his feet. That rifle was a bit more than I cared to pack. The fellows I was hunting with packed it for me some on the pack out because my pack was full of goat. They also complained about the rifle's weight. But again, that was hunting in the mountains where the mountain goats live,about 6 miles in from the road.
Lighter contoured barrels can shoot pretty darn good for their first two or three shots in my experience. Then the barrel starts to heat up and the groups from a thin, light barrel will start to open up in comparison to a heavier, thicker barrelled rifle.
My rifle weight goal is a bit of a compromise. I'm willing to pack a little more weight than an ultra-light rifle scope combination because I'll be attempting shots at far greater ranges than most other hunters packing around their 6 lb rifles. I think the additional weight help's to control the shots at longer ranges. If you're going to shoot at less than 500 yds, the lightweights will generally get the job done and that would be ideal for a lot of back-country packing, particularly in the mountains. I decided I'll carry a couple extra pounds of rifle/scope weight for the added accuracy out past 5-600 yds. My rifle scope combination will likely weigh around 9 lbs, in part due to a 25 plus ounce scope/ring attached to the rifle. But lighter scopes will also work if you're really putting on the miles in the rough country. Now that I'm older, I don't push myself as hard as I used to, and an extra pound or two isn't as energy draining if you're not on the move from daylight until dark.