This is an interesting one. You have top two pair on a rainbow flop. There seem to me to be few hands you are behing. AA, KK, JJ and QT. All of these hands are possible, some people would reraise AA or KK but the hand is already headsup at this point so he may be trying to trap you. JJ is an obvious caller preflop and QT probably is from the BB as well. Against all these hands you are a massive underdog, drawing dead or to 4 outs.
The far more likely scenario though is that you are way ahead and should be looking to extract as much money from him as possible. He may have a gutshot draw if he has a Q or a T but I personally don't think this draw is worth worrying about too much. Perhaps I am a little reckless here but I'm not too worried about letting someone draw to a gutshot here since if it hits it's pretty easy to see.

given all this I think the best thing to do is check in behind him and hope to induce a bluff on the turn. If he makes a pot sized bet on the turn I push provided turn isn't a J, T, or Q in which case I'd call.
If the turn blanks and he checks, I'd make about a $400 -$500 bet hoping for him to checkraise me.