PREFLOP: Given that the action started from early position and its been raised and reraised, you shouldnt been in love with your hand at all, but becuz you have a discount by being in the BB, you should call IMO. Capping in this spot without reads would be over the top.

FLOP: Standard

TURN: Something funny is going on here. Two people go bananas preflop and this is the kind of board that should atleast compliment one of their hands and then they both check the flop. I think you should check again on the turn with the intention of folding again, somebody is either slow playing a monster, AA,QQ,AQ or somebody has KK and they probably wont fold. So I like your turn check.

RIVER: Checking again is the right play. You cannot bet this river becuz although the chances are higher that you may have the best hand given the previous action, it will be hard for you to get called by a second best hand, you are still better off checking and calling.

Overall you played this hand as well as you can play it.