My custom 7mm Remington Magnum with an 8.5 twist 24" Hart barrel with suppressor, blueprinted to a 700 Remington stainless action and Jewel trigger coupled with a Nightforce NXS 3.5x15x50 scope, coming in at a little over 9lbs, is my favorite elk and Muley rifle.
For straight long range shooting I also enjoy my custom 300 RUM. But it is almost 15 pounds, sporting a 30" LW barrel. Although I have shot a few deer and an elk with it, I don't want to carry it hunting. The kills I made were from a place I could drive my ATV to and set up.
I also have a newly built 6.5 PRC that I like the way it shoots and its lighter weight but, because both deer and elk are open at the same time I usually hunt, I prefer the 7mm for elk because it anchors every one I have shot.