I have a factory 30-06 barrel at home that I will weigh this evening and post back up. It may be a 22" barrel (I can't remember), but it should get you in the neighborhood.
I know this is almost 5 years old but I found it extremely helpful and thought I would add I saw on another forum that the 24" in 300 WM is 2 lb 5.5 oz.
I'm trying to find out the weight of a T3 in 308 Win and a T3x in 223 Rem. Trying to decide if it's worth upgrading to a CF proof, given the weight savings is all I am personally after given the stock barrels both shoot as well as I would need for hunting. Believe both of these barrels are 22.4" long.