Lead the turn. Yeah it's a scary card but you have no real idea where you're at if you check, and you can't automatically assume when a draw card hits that villain has completed his draw. If you're calling a push after checking anyway, why not bet out yourself?
Big overbets usually mean "I don't want to be called". I may call here expecting to be shown AcX/KcX pretty often (I haven't looked at the results yet), however it may also be reasonable to fold and see what he shows down after big overbets against others. If he is betting big with air you'll hopefully be able to find a better spot to play back before he goes busto, if he overbets with big hands you might be able to push him out of pots when he bets small, and so on.
Basically, I don't like getting into situations like this without reads, but the typical micro-donk is capable of pushing such a huge range of hands here I guess I could find a call if I looked hard enough.