Well, the lightest options that exist with adjustable cheek are the XLR Element V4 magnesium (min 28oz), and the MDT HNT26 (min 26oz). Neither of them has an adjustable buttstock in the lightest configuration, but the pads can be removed and replaced. Please note that the lightest stock options, once you add bottom metal, are about the same weight but don’t have adjustable cheeks.
As such, if you want adjustable, you’d probably need to get one of the adjustable buttstocks that either manufacturer offers for an additional pound or more in weight, or get the KRG Bravo for about the same mass hit. Or get a replacement adjustable buttplate that also adds about a pound.
With the understanding that it adds literally 50% weight to the chassis, how would you feel about adjusting scope and cheek position instead?
