My coop has served well for 5 years with normal screens on the windows and 4' poultry wire enclosing the coop (inside a former equipment shed) and hen yard.
Weasels are common here in northern Maine. A few weeks ago, I came literally nose-to-nose with one in the garage, in early afternoon. That was a bit too close for comfort -- and it explains the disappearance of the squirrels that had moved into the garage.
When I rebuild the coop next month, all entry points will be shielded by hardware cloth. That little critter was totes adorbs but I just knew while we stared at each other it was thinking, "If I tear your face off, I'll eat like a king!"
So far I have lost two hens to a fox and one to a hawk. The hens are now confined to the Henitentiary (6' chain link fencing enclosing a 30' x 40' yard) with clipped wings, and their coop will be hardened well before my new chicks join the flock.
I recommend as much hardware cloth as you can afford. IMO, it's better to have it and not need it than need it and not have it. If you do have visits from a weasel or two, you don't want to know about it.
My outer walls and windows will all be covered with hc, and the inner divisions will be separated by plain old poultry wire. As time goes on, I plan to cover the bottom foot of the chain link with the old poultry wire and extend it out at least several feet outside the yard. I'll put some soil to cover it and scatter rocks with plantings between them. (The most prevalent crop in Maine is rocks...)
Good luck!