Too passive with JJ or well played?

[The Setup]

This is my third or fourth hand at the table so no reads.Looking for opinions on this hand I played earlier. I felt I was a bit too passive post flop and wanted to stick in a raise somewhere post flop.I would usually bet out on the flop here however I didn't want to bet out against a three-bettor pre-flop. I was thinking MP could have an overplayed AK but I just wanted to get to the river cheaply.
How did I do? All comments appreciated



dealt to Hero [Js Jd]
Hero: raises $4, UTG+1: raises $6, MP: raises $8 (2 calls three to the flop)

Flop: [4s 6s Qh]
Hero: checks, UTG+1: checks, MP: bets $2 (2 calls three to the turn)

Turn:[4s 6s Qh][9c]
Hero: checks, UTG+1: checks, MP: bets $4 (2 calls three to the river)

River:[Jc Kh 6d 4h][6c]
Hero: checks, UTG+1: checks, MP: bets $4 (2 calls)

[well]

What happened at the river?

[The Setup]

Sorry forgot to add that UTG+1 mucked, MP had Tens. MHIG

[MisterKing]

This is 2/4, right? I guess with it being capped PF, you have to give some credit to the raisers to your left. That said, you gain no information from your check/call on the flop and turn, and may be leaking extra bets by doing this.

An alternative might be to check-raise on the flop, and see if they 3-bet you. If they do, my play would be to call the re-raise, and go into check/fold mode if unimproved at the turn. This way you're gaining a lot of information, and doing so on the cheap... the cost to you is one extra small bet if they just call your flop check-raise, and two extra small bets if they re-raise and you call. Your strategy of check/calling along to the river leaves you exposed for 5 SB with any number of hands ahead of you (KQ, QJs, KK, AQ, 66, 44, etc.) and no way of knowing.