Definitely check with your game regs, weasel are considered "fur bearing" in most areas and may have different rules for taking them.

A neighbor of mine used to have ferrets, which are weasels, and even "descented" they stunk a little. Whenever a domestic weasel set up camp and started to scope outmy late grandpappy'schicken house he'd turn loose what he called his "weasel dog", usually a beagle. He explained the training process for making such a specialized critter as follows: "Boy, what you do is git yerself a half growed beagle pup and put him in a rain barrel, then ya live trap a weasel and put him in with the pup and hold the lid down tight. You'll hear a gawdawful racket for awhile, then it'll git real quiet in that barrel. Once it goes quiet ya lift the lid and see who won, if'n it's the weasel ya shoot it, but if'n it's the pup he'll be a mite tattered but he'll also hate weasels for the rest of his life."

He was right, every beagle he ever had hated them and would mercilessly track them down if they caught the slightest whiff of one in the breeze.