Re-raise PF and you will have control of the hand instead of him. A loose player 5-handed will raise with almost anything, so JJ is miles ahead of his range. When he bets 50c into a $3 pot, he most likely has a draw (donks usually aren't clever enough to do this with a set or two pair). Make a pot-size-ish raise. If he calls, slow down (check) if the turn completes any draw (as it did here). I'm inclined to fold the river because his play really really looks to me like he has the K. From his play I say he has KT/KJ. He is probably overbetting the river because he thinks you have AQ/AJ/AT or a set. He would not overbet the pot if he DIDN'T have the K because there was no indication from you that you could not have one as well, you simply called the entire way through. Be more aggressive with big hands against loose players, you are ahead of them a huge percentage of the time.

As played I fold the river, you have only invested $1.50 and like I said above, it would take balls of steel and a brain of mush to overbet without the K here. He made that bet hoping you had a big 2nd-best hand, and it turns out you did.