Best to start with a Remington 700. I love Rugers and own more of them than Remingtons, but they will never be lightweight.
Bingo ^^^Ruger 308 Hawkeye stainless all weather. 22" Barrel fluted, bolt handle skeletonized (as best it could be), bolt could not be fluted, it's a two piece bolt. As is, with a Leupold VX2 2-7X33 and sling. 7lbs 14oz, probably right @ 8lbs with 4 cartridges. Factory full zytel stock is 1oz
lighter than the factory boat paddle, skeleton stock.
In contrast, Remington SPS stainless all weather 257 Weatherby Mag.. 26" barrel fluted, bolt fluted, bolt handle skeletonized, factory stock. 6lbs 2oz, no scope. With a Leupold 2-7X33 it would be 6lbs 14oz, 7lbs all up. I put a Burris 2-10X40 Euro Diamond on it, I think that scope is 22-24Oz. Still lighter than the short action 308 Hawkeye.
Although I like the looks of the Hawkeye, it's all esthetics, and I would not spend the money to do it again.