The entire run including the roof, floor and underneath the coop will be done in 1/4” hardware cloth. Heavy predator area and we have seen a few weasel/ermines in the yard.
Most people around here recommend the 1/2" hardware cloth instead of 1/4". It's a stronger gauge and sufficiently small.
Be careful with hardware cloth under ground where chickens will dig. They can easily get down 12" and it won't be good for their feet if they get to it. Consider an anti-dig apron around the perimeter or going straight down a foot or so around the perimeter.
That said, I don't have weasel pressure, so feel free to reach out to those with more experience with that predator.