Rats always tried to burrow under my colony and they can climb just about anything while fitting through surprisingly small openings. After years of attempts at various methods I ended up having to put out bait stations and just poison them. Not the first time. I tried every other method when they got in the chicken coop and then with mice in this new house. DIY plaster bait works ok if you keep replenishing it regularly since it doesn't work fast or with just a single bite. It won't transfer to anything that eats rodents and it won't kill larger or many other types of animals but it simply wasn't enough with the numbers I keep dealing with in my area. I always end up putting some very sturdy bait stations and rat poison out year round. It's just not worth the damage (still have wiring in the house that doesn't work right) or death of kits and other small animals to mess around with traps and alternatives to commercial rat poison.
Small weasels can be possible and would likely be easier to trap. I've never had one small enough to mistake for the rats. We did end up with a fishercat. Some have been coming down from Canada to the northern US and they are darn near impossible to deal with. Large weasels with the ability to tear wire, dig, climb, and tend to maintain large territories with randomly spaced attacks while also avoiding most traps. I gave up on free range chickens when that appeared but ended up moving in town a year later anyway.
