Choose a short-barreled, lightweight, short-cartridge rifle (Or lever or single-shot). The ammo load will also be lighter.
I used my Savage scout for backpacking this year. In 308 it is enough for elk, and the ammo is lighter than other choices.
If you are willing to use a single shot, and reload, you can build some very light rifles on T/C Contender actions. I have a .358 ALPO that weights under 3 pounds with scope. And, none of the components is exotic except the custom barrel. Leupold scope, Choate stock, and a Dave White
http://www.dandtcustomgunworks.com/ barrel with an aluminum muzzle brake. Power level is similar to a 356 Winchester, but you can use pointy bullets, I use 225 grain Noslers.
I used the Savage this year because I moved and did not have enough 358 ALPO ammo, but the rain is starting so I should get some reloading done this winter.
