I think once you check the turn, his line is good.

You aren't checking the turn here with a strong hand. You might check the turn here wtih Kx, but once he min bets you'd for sure raise him for value.

So you either have air on turn, and his minbet could be inducing some kind of bluff, or a value raise. Or you have a draw on turn and likely a weak draw that wasn't strong enough to bet yourself. Obviously he wants to let you get there.

I'm not saying he thought about any of these things when he minbet you. But once you check the turn, a very small bet is prob best given what you're repping.