even the preflopraise and flopbet is weak. He raised to 1$, you call and the 0,50$ of the limper and BB make the pot 3$. He bets only 1/3. Ok, maybe this is his standard value bet size but he should bet bigger pre and postflop to get value. You can have a lot of small and middle PPs, probably no Kx but maybe you peel one of with your PPs because he would cbet his whole range on this flop.
And there is no way you fold the turn. It looks so much like a blocking bet. Think about the hand from his point of view: If he has Kx he won't call the flop because he puts you exactly on 7x and is hoping to hit a K and is now afraid that you will check behind. He probably calls the flop because he thinks you are bluffing
and will let you continue.
Call the turn and bet the river if he ck to you and if he bets very small again on the river I would raise for value because now it's certainly a blocking bet or just call if you are really a bit afraid