Is your goal to simply keep out hawks/eagles, or do you need stronger protection from climbers like raccoons? The difference in need is going to make a huuuuuuge difference in price. If you need to keep ground based predators out, you need to use hardware cloth, like you do for the walls. May be able to get away with some 2 by 4 inch farm fencing for a roof, but that will only stop the larger predators from climbing and then squeezing right in. Pricey if you need to go that way. If all you need is flying predator protection, you can't go wrong with some simple (and extremely light) plastic deer/bird barrier. The type used to protect fruit trees and veggies from being eaten by birds.
My run is about 15 by 25, with large cherry tree in the middle, and I was able to use a 30 by 30 foot single piece for most of it, cutting smaller chunks from another roll to fill in around the tree and in odd shaped areas. One benefit I found to using the thinner and lighter netting is that it is visible enough to the hawks, but not super obvious to humans. So it doesn't look "ugly". Available in various sizes on Amazon.
