According to their web site, BKL #257 rings weigh 2.2 oz. These work very well with 1" dia scope tubes and Anschutz 11mm grooves. And FWIW, I've never known BKL rings to mark a scope tube.
But are you really sure you need to go that light? I have a 1710 MC with Burris Signature rings on a BKL riser, Leupold VX III 6.5-20 scope, and have no trouble at all making weight.