I'm sure you have already looked at the cartridge drawings and seen that a rechambering job will work for this cartridge (encase you didn't, I did & it will). I'm not sure of the thread size, count, and pitch for the weatherby barrel, but if you are not successful with this post, make a new one asking the thread size for both barrels (Weatherby & Browning). I'm sure this is going to vary depending on the exact model, so have that information ready and included for both barrels/actions. If the weatherby is the same thread (diameter, count, and pitch) then you are good, if it is same dia. but different count then you've got a problem. If it is larger, then it might be able to be turned down and re-threaded to fit. This is done very easily when taking a rem. 700 barrel and putting it on a savage 110. Sorry I don't have the specs. on the threads for either action. Good luck!