While the above mentioned rifles are fine for the average hunter, your requirements are putting you in a very specialized arena.
Something like the Tikka & Kimber Hunter would get you closer to the weight your looking for, but bare gun. Not scoped.
Only 2 rifles & manufacturers come to mind for a true, under 7lb scoped rifle.
Both will set you back about $3,600.
First pick would be a New Ultra Light Arms model 24B.
Weight with Talley rings 5.5lbs.
Second would be a Proof Research Elevation Light Weight Hunter at 5lb 14oz.
Add a Burris Fullfield E1, 4.5-14X42 and a nylon sling, and your right at 7lb.
I should mention that with these ultra light weight rifles, most find shooting from a bench to sight scope in, do load workups can be a bit heavy feeling in the recoil deptartment. Standing/sitting with game in the scope, you don't notice it as much.