I'm curious, why did you lead out with half of the flop's bet on the turn? To a more agressive opp, that'll signal weakness and they'll put in a bet you can't call, regardless of holdings.
So would the correct play be to check and fold to a bet? I figured a smaller bet would be raised by a set or a king and I would have folded there and then if it were substantial. I thought the fact they called indicated they were on a flush draw.