We don't have weasels. We do have raccoons. opossums, bobcat and coyotes (and dogs). The Larger animals probably aren't going to bother coming to the barn with the horses there, but the racoons and opossums have no boundaries. The coons are masters at tree climbing, so I have no doubts that they can scale a wall and climb over the top of the coop.
You may not have SEEN them but you HAVE them:
http://collections.burkemuseum.org/mamwash/carnivora.php
We saw an Ermine (short tailed weasel) near the house in the fall 2 years ago. Cutest ****** thing, pure white but the black tip on the tail, black eyes and nose.. Then I went down to the barn and covered the dirt floor of the chicken coop with 1/2" hardware cloth run up the sides and poultry stapled. Then put the horse mats back down.
Bruce