As a big fan of Proof barrels, i'd skip it and just get a medium palma, rem varmint/ sendero, or marksman contour. Weight difference between those contours and a Proof CF sendero contour would be about 1lb to 1.5lbs or so +/- some.
For the chassis, per XLR the carbon chassis would be lighter than the Manners with elite fill and mini chassis but not by any amount to make a difference. The KRG Bravo would be lighter than both until you start adding stuff to it they're all almost a wash.
For reference: My 6.5 Saum is 15lbs 11oz with a 26" sendero contour in a KRG W3 folding chassis w/ enclosed forend and full length dovetail, S&B 3-20x US, Badger PSR mount, 7rd Alpha Mag and Atlas Cal w/ RRS btc pro mount.
My 308 is 13lbs 7oz with a 21" marksman contour, KRG Bravo w/ W3 forend and full length dovetail, Minox ZP5 5-25 in ARC medium rings, 5rd AI mag, and the same Atlas Cal in RRS mount.
My 6.5 Creed is 12lbs 8oz with a 22" Proof CF sendero contour, Minox Zp5 3-15 in ARC mediums, Manners PRS2 with barricade mini chassis and RRS dovetail, 5rd Ai mag, and same Atlas Cal in RRS mount.