I don't really know much about weasels, though I've looked for info. I worry about them with the chickens, rabbits, and young geese. My chickens and rabbits are pretty well protected (at least at night -- the idea of weasels hinting in the daytime is discouraging!)
however my young geese are in a house made of 2x3 wire, which of course won't keep out snakes or weasels. What I did was take the vinyl mesh that I use for hawk netting overhead. It has 1/2" squares. I covered all the wire with that and buried the ends a bit. I'm not sure if weasels would chew through it, but if not it should keep them out. It's very inexpensive so I mention it in case it can help?
I hope the dog helps as well I have my geese in a fenced yard used by a dog, since my real concerns are coyotes, raccoons, and the like.
Whatever it is, I hope you don't have any more problems.