Ive dropped quite a few M70's in Brown, Bansner, and McMillan stocks,ditching the factory lumber in the process. I don't care what calculations on the Internet say....you WILL save weight.
My favorite in a 270-280 is the Brown PoundR. More expensive and the kevlar is supposed to be tough to work with. Very rigid. They last a very long time; for most a lifetime of hunting and shooting IME.
Very tough to beat them for weight.
If you want to get a light M70 you must watch everything; barrel contour,bottom metal, stock, mounts.etc. Ounces add up fast when you start with a heavier action. No one component will do it but the barrel and stock are major factors of course.
No matter what you do to them they will never be a Kimber or Ti Rem 700. Just the way it goes.
For a 270-280, a target weight of 7-7 1/4 should be doable if you watch what you are doing.