my profile pic is the lone live weasel I have seen, he was loping across the yard and when I went out to see what that skinny, long chipmunk was.. he climbed a tree and posed. 4th gen on this farm and no one remembers weasels around.I vote rat. Could be a small ground hog, though little motivation for a ground hog... though they do like chicken feed. I've recently discovered that there are rats in my yard: garden, wood pile, HK mound. Have not seen any tunnelings in/around chicken run... yet. Squirrel, chipmunk... See if you can set up several different types of traps. Of course keeping safety of other critters in the forefront of your set up. Good luck. Rats are wary, and smart, so you may have a difficult time catching one.
Edited: Weasels are found in all 48 states. You are not likely to see one... but you will certainly see their damage if you don't build your coop to exclude them. I don't think they are burrowers. They use holes left by other diggers. Though I could be wrong here. I've been told they are not climbers, yet a google search showed footage of one climbing down out of a tree. If not a climber, how did he get up so he could then climb down?