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.
Good Luck,
Don