When you flop top set in a 3-bet pot, checking back allows your opponent to bluff or catch up, maximizing your value on later streets.
Checking back top set is the preferred strategy here to protect our checking range and trap Villain's air.
Note: Betting is fine, but checking back top set on this board is a higher-EV trap, allowing Villain to bluff turns with their many overcards.
Calling the check-raise is mandatory; we have the effective nuts and want to keep Villain's bluffs wide.
Checking back the turn is the standard play to continue the trap, though shoving is a viable mix to deny equity.
Note: Shoving is slightly lower EV than checking; Villain has checked again, and we want to let them take one last stab at the pot on the river.