I've taken notes on most of the guns I've had apart at one time or another.
29†Savage 12 BR barrel .308 Win
◦ Straight taper from full diameter to 0.900†@ muzzle
â—¦ 5.93 lbs (5lbs 14.5 oz)
For comparison:
30" Savage 12 F/TR barrel .308 Win
â—¦ Straight taper from full diameter to ~0.990" @ muzzle
â—¦ 6lbs 10 oz.
A typical 30" Heavy Palma contour barrel from various makers (Krieger, Bartlein, etc.) has a 2.5-5" full diameter shank, a radiused section, then a straight taper to a .900 muzzle diameter and weighs in @ around 6.5 lbs, give or take a bit. If you stick with a barrel nut, that 'shank' section will get reduced from 1.250" to 1.130 to clear the barrel nut, and will weigh slightly less. There are ways to keep the full diameter and leave a small reduced section for the nut, but personally I think that looks silly.
Depending on how tight you are on the weight limit with your scope, rings, bipod, etc. you could probably get away with just going with a 30" 'bull' or 'target' contour i.e. what the factory 12 F/TR barrel is. If you're fine with barrel nuts, I'd suggest looking up Jim Briggs @
Northland Shooters Supply, and ordering a pre-fit barrel from him. If you want to go nut-less, then you have other options (and issues) to deal with.