Unless I just wanted to spend more money one of the Ruger Americans in any of the short action calbers will come in under 7 lbs with a Leupold scope. The 7-08 or 308 won't beat you up in a rifle that light. You'll never notice the difference in performance compared to 30-06 which will beat you up in a 7 lb rifle.
Can't say a bad thing about the Tikka. In fact it might be a smidge more accurate, but we'd be talking fractions of an inch in group sizes. The Ruger is just as good IMO for a lot less money in a hunting rifle. If my goal were tiny groups at long range I'd give the edge to Tikka..
The Kimbers are great rifles, I have one in 308. Mine is just a hair under 6 lbs including scope. Recoil is exactly the same as a 7.5-8 lb 30-06, which ain't too bad. The mechanical accuracy of the rifle is every bit as good as anything I own, but I simply shoot something around 7 lbs better. I've chased light weight since a backpack hunt in the 1970's with a 9 lb rifle. The Kimber is a great choice where every ounce counts. But as a general purpose rifle I find a weight of 7-7.5 lbs to be a good compromise.
