$10 NLHE 6-max: AA on 3way wet low card board

I have AcAs UTG in a 6-max table. Open to 33c. Two callers, CO and BB.

Flop comes 5d4h6c.

BB checks, I cbet 2/3 pot. Both call.

Turn is 3c. Everyone checks.

River is 9h. Everyone checks.

Cbetting the flop but checking the later two streets ok line for me?

im going for bet turn so that SD/FD will pay and analyze river

I wouldn't bet the turn because you are making the pot unnecessarily big and your relative hand strength is not that outstanding, especially since you are 3 way in the pot.

Therefore, I think the check is correct and if you are faced with a bet on the river, I would pay a lot of attention to the bet size. After all, your opponents have a very small bluff range as played.

Some boards are just vey bad for big pairs.

If you had only 1 caller on the flop, a barrel on the turn would have been OK (I still prefer a check). With 2 callers on the flop, I think attempting to check the hand down is fine.