If you are really concerned about weight, and I think you should be, I'd worry about long range capabilities of the rifle last.
I'd build something that I could shoot well first.
Rounds like the 7-08 or the 7X57 kill very well out to 400 yds. If you build something with more recoil than that, you may well find that it is tough to shoot well, not at all fun.
6.5 lb. '06's I find to be a bit much, even from off hand. From prone, or over a pack, they wouldn't be anything I'd want to shoot much.
So, I suggest you try out a few in these weights. Once you learn what works for you, then go for a build. E
