A weasel or mink is incredibly fast, and would catch even a free-ranging chicken in a heartbeat. After all, they are predators, and they do this for a living.
Weasels especially are very hard to keep out of a cage/enclosure. They can get through a hole not much bigger than a nickel, and once inside, they will kill till there's nothing left to kill.
Some seem to think that it's wrong to humanely dispose of chicken killing predators, because they are only doing what comes naturally. I disagree. Killing frogs, snakes, grasshoppers, wild birds is what comes naturally. NOT killing chickens. Once one of these predators finds out how easy it is to kill domestic birds, they will be back till there is nothing left to kill. So, in my opinion, those predators that have learned to kill domestic animals should be removed from the gene pool, and the ones that actually do what nature intended will prosper and reproduce.