Pests that attack the curly willow can include gypsy moths, aphids, lace bugs, etc. Fortunately, other bugs will eat the aphids. For the other pests, fertilize & water tree!
Proper fertilization usually helps get rid of and prevent them. You should also try infrared treatments. They will kill the pests without hurting your tree. I don't recommend pesticides for your problem.
You will need to get a specialty pest spray from a farming supply depot or the internet. You need to spray when the chrylassis (cacoons) have formed. The catipillars in question are resiliant to the spray.