I put up bird netting on top of my chicken run. Bird netting is pretty inexpensive. I live on a lake and have hawks and Bald Eagles overhead all the time. For the past 3 years I have owned my chickens, there have been no attacks from haws or eagles with my bird netting in place. A solid covered roof for my chicken run would be too expensive because I would have to build it strong enough to withstand our snow loads. Anyway, the bird netting prevents attacks from the sky.
It sounds like you had a hawk attack, but if it was a weasel, then you have other concerns and the only thing I know that can keep out those varmints is 1/2" hardware cloth all around with predator netting on, or in, the ground to prevent digging. But it sounds like you had a hawk attack. Good luck.