I built a 338-300wsm around a Win M70 short action. Pac Nor 24" ultralight barrel, bell and carlson medalist stock. I've run a few different scopes which change the weight around, but I want to move to a VX3 LR 4.5-14x50 and the new moa reticle, w/ Talley rings. That should bring the fully outfitted setup to right around 7.5 lbs. It's a dream to carry and kicks like a mule.
If I were to build it all over again, I would use either a McMillan edge fill stock or one of the new lightweight Manners stocks. The lighter stock would let me move to a little heavier barrel like a #3 fluted which would help tame the recoil/jump by moving mass to the barrel.
Good luck on your build, 280 AI is a sweet round. I think a rifle in the 7.5 pound range would shoot and carry/balance very well. A 280 AI could be a bit lighter, but any light rifle is going to kick so be careful! If you really want to go extreme on weight, then a brake might be a good option.