As a number of you know, I picked up a Ruger#3 in 45/70 on this Forum. It is light enough for me, however, I am just a young feller
(age 70), and have never been bothered by rifle weight. The previous poster who suggested getting in shape has the right idea (I haven't been in shape for a rather long time, as my friends will attest

). That is the real answer, of course.
The back side of light weight is recoil. My little #3 will be used mostly with 300-350 gr bullets (largest game for me will be white tail deer). Five hundred grain bullets in the #3 at the velocities attainable in that strong action will make your "eyes bulge" and slam you to your toes. Recoil is rather grim

. However, when hunting, you normally don't take more than one or two shots (one is what I strive to do as I am sure most of you do, also). You can stand quite a bit of recoil if you don't shoot long strings.
On the other hand, I have long admired the .257 Roberts for a "power package" with light recoil. It seems to me, that particular caliber (.25) represents the bottom floor of consistent bullet performance on the lighter big game. I am thinking of deer, sheep, black bear, etc. I have a couple of these rifles and truly admire that cartridge. There are terrific GAME bullets available as well as light varmint bullets that will do what you wish. The various 6mm's have had numerous "bullet" failures that somewhat reduce my desire for that caliber as a light big game rifle. I have been in on about 70 black bear autopsies and while my experience pales in comparison to a number of you fellows on this board, it has been enough to give me an idea of the bottom limits of a good big game rifle (mostly, lighter big game).
Dale53