This rig weighs 12.5 lbs with the sling and bipod attached.

It's a Rem 700 SPS Varmint 308, 26" Rem varmint bbl. HTG stock with sniper fill. Alloy Badger M4 bottom metal, Leupold MK4 3.5-10x40 in Burris Signature DD rings/base.

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It should be easy enough to hit your desired max 11 lb weight, with edge stock , flutes, and a sensible sized scope.