When in college during the 1970's I got a chance to hunt some really steep terrain and cover a lot of miles each day. I've been chasing light weight rifles ever since and have tried a lot of different ones. I bought one of the 1st lighweight fiberglass stocks from Brown Precision in 1983 to lighten up my rifle. Some observations. I prefer a barrel with a little more meat in it and generally like 22". Weight is better reduced elsewhere. "Quality" synthetics are the only way to go. Most cheaper synthetics don't weigh any less than wood, and many weigh more than wood.
A Winchester Featherweight was a light rifle by 1950's standards, but today it is on the heavier end of spectrum. Plus most of the weight loss is in the skinny barrel. I've had 2-3, but just never warmed up to them.
Your Remington Mt rifle certainly has potential, and at just over 7 lbs is a good weight. I normally don't like laminated wood because it is too heavy. But that is a trim design and the rifle is light enough. I've had a few of those over the years and were things I liked about them. The barrels are thinner than I prefer, but all that I owned were pretty accurate for 2-3 rounds. After that groups opened up considerably, but I never considered that a handicap in a hunting rifle But I can't afford to keep everything I like so they went down the road to pay for others that I just liked better.
I've come to the conclusion that somewhere around 7 -7.5 lbs including optics and mounts is a good place to be. I have a Kimber 308 that can weigh under 6 lbs with the right scope on it. Currently 6.25 lbs. It is a good choice for extreme terrain, but I think it too light as an all around rifle.
For the money I think a Tikka is the most rifle out of the box for the money if you want light. Even with a decent sized scope weight can be kept right at 7 lbs and they still have a beefy barrel which helps balance and accuracy.
Some of mine, The Kimber, 308 in factory stock. 6.25 lbs as shown.
A Winchester 70 Sporter 30-06 in a McMillan Edge stock. Is 7.5 lbs as shown
My all around rifle. Winchester 70 EW 308 in a McMillan Edge stock, 7.25 lbs as shown