Good advice already given but if you want a truly light weight rifle take a look at the new hunter model from Kimber as it will come in at 5.65 pounds without scope.
http://www.cabelas.com/product/KIMBE...ES/2318549.uts
Having said that , shooting any of the 300 mags out of such a light weight rifle may not be that much fun so I would look at a 308 as it will do anything the magnums can do unless shooting past 250 -300 yards then the magnum would have the advantage. Epps has one in 308 for $1228.69 and the Kimber's also come with a sub MOA guarantee and are really nice rifles with controlled round feed on a scaled down Mauser action and a 3 position safety that I really like.
https://ellwoodepps.com/kimber-84m-hunter-142593.html
Although many rifles will fit the bill of what you are looking for you will be hard pressed to beat the Kimber in the weight department . This is my Kimber classic select 257 Roberts fully loaded and it is a dream to carry and shoot.
Happy shopping.
http://i78.photobucket.com/albums/j1...ps92p1hjw9.jpg