"I have to use pesticide ..." To be honest I don't think you do. Buddleja is a tough plant and can easily recover from some insect damage. The whole thing will be cut down regularly anyway. Being a major attractant to butterflies, and as you say, hummingbirds, I do not not think it is a good idea to use any pesticides on it. If you don't like the look of it I'd just cut off the most affected parts.

p.s. Mullein Moth will attack Buddleja.

This damage is really minor. If you want butterflies --- and Buddleia is called "butterfly bush" you have to tolerate the damage of their caterpillars. To have butterflies, caterpillars --- which mostly eat leaves --- need to thrive.

Drooping is probably excess or insufficient water.