Free: Contests & Raffles.
I recognize the greatness of weatherby cartridges but have no desire to own one
Tikka T3 fits your description very well. Light, relatively inexpensive, and accurate out of the box. Get a 270 WSM or 30-06. It will kill elk at 400 yards, but be reminded that it requires someone behind the stock with practiced expertise to ethically do so.
why don't you spend $250 and get a 300 win mag barrel for your encore and call it good? mine with the bull barrel and a 4-12 vortex scope weighs 8.6lbs on my bathroom scale....it carries really nicely. you could get a pro hunter barrel which is fluted and loose a few ounces.