In a stone shed I would line the bottom two or even three feet (depending on how it is getting in) with hardware cloth.
You could do an inside or outside layer of hardware cloth.
An inside layer would be set up like a bathtub liner.
An outside layer might be easier, but don't forget to either bury the edge deeply, or flare it out like a skirt.
I am super sorry for your troubles.
Weasels are horrid!
If you simply can't figure out how to do the hardware cloth (and it needs to be hardware cloth, not a wire with larger holes, those weasels can squeeze themselves super small) then ..... Uh......... I can't think of what kind of animal eats them.... But maybe you could try to trap it.
