The Kimber will be about 1-3 lbs lighter with a scope on it than a lever action will weigh with no scope. Depending on which lever action you decide on. My Kimber is still under 6 lbs scoped, all of my Marlin 30-30's are the heaviest rifles I own. Even my lightest lever, a Winchester 94 is 6.75 lbs and is heavier than my 300 WSM bolt gun.
Despite the myth, all things being equal lever actions are the heaviest rifles made, bolt guns can be built the lightest of all actions.
If you are interested in nostalgia and aesthetics lever actions are the way to go. If you want performance, better prices, much better accuracy, less weight, and far better reliability one of the trim bolt guns is the answer. Kimber or NULA are the lightest at around 5 lbs and most expensive. There are lots of more moderately priced bolt guns right at 6 lbs that would weigh around 7 lbs scoped. There are darn few levers under 7 lbs naked and many are 8-9 lbs. None in center fire calibers under about 6.5.
A round such as 260, 6.5 Creedmore or 7-08 will recoil much less than 44 mag or 30-30 and be more effective at 50-100 yards than 44 or 30-30. Would also be effective at 500 yards on deer, at least 400 for elk. A 308 would have a bit more recoil, but very little more than 44mag or 30-30.
FWIW I own more lever guns than all other action types because I like them a lot. But when it comes time to hunt they stay home in favor of much better choices. Unless I'm just in a John Wayne kind of mood.