Thanks guys for all the responses. I guess I should have been more specific about the recoil. Shooting a rifle a few times won't make me flinch. It's when I take one out to the range and really put some lead through it, trying to shoot it from different shooting positions. I'm talking about a 15-25 rounds.
I have a .270win Winchester model 70 (8 1/2lbs estimated) no problems with recoil. The 7mm rem mag mentioned before (10 3/4lbs) no problem. While on the other hand, I have a 8 1/2lb Ruger m77 in .338 win mag that my brother gave me after he won it in a pool game. I can shoot this gun effectively out to 250-300. But after about the 5th or 6th shot...you guessed it: flinching time. I never really did that before I got scoped but now I can't seem to break it. I just didn't want suggestions for .300 mags or above for a 6-7 lb lightweight rifle. I want something I can shoot comfortably and get very good with it.
With that said I'm going this weekend to hold some of those models that I mentioned. I'll probably buy online but I want to handle the rifles and see which one feels natural when shouldering it. Out of the 3 scoped big game rifles I own the ruger seems to just fit me the best. The Remington Sendero is the most expensive but the Ruger just seems to feel better, like it was custom made for me. Too bad its .338 win mag.
Keep the suggestions coming guys. I'm leaning more towards the .308 or .270wsm. The 7mm-08 just seems a little light to me for when I draw an elk tag. Hell I'll admit I don't really even need a new rifle, I just want one!