A weasel is A LOT smaller than a raccoon and can fit through some very small spaces. Depending on the size of the cage wire on your trap, a weasel may be able to squeeze right through it once it is caught. Another consideration is the sensitivity of the "pan" (the part of the trap that the animal steps on to trigger the door closed). Obviously a weasel is going to be much lighter in weight than a raccoon or a skunk and the weasel may not even trip it.
That being said, weasels are quite easy to trap as they do not fear humans, similar to a raccoon or skunk. Not like trying to catch a fox or a coyote. I personally have not ever caught a weasel in a live trap, but have caught plenty in other kinds of traps.
Good luck in your weasel quest. They can be mean little critters, its surprising how much damage such a small animal can cause.
The best bait for a weasel is a livr mouse, which you can buy at any pet store. As stated before, they are small and can fit though most live traps. I have caught many in a rat trap, which can be bought at your local hardware store. I know of some that have even been caught in a large glue trap used for for rats. I don't like the glue traps for they give off an odor that may cause the weasel can smell and avoid. Place the mouse in a cage at the back of metal box that the weasel can't get pass, then set the trap in the front of this box. If the weasel comes around, you will find it in the trap, they can't pass up a live mouse.