While 66 is an overpair on this low flop, checking back preserves its value as a bluff-catcher and protects our range on later streets.
Checking is the preferred play here. While we have an overpair, betting 66 often isolates us against better hands (77-AA) while folding out the air we want to keep in.
Note: Betting here is slightly thin; checking back keeps Villain's range wide and protects our checking range on a board that favors the 3-bettor's high cards.
Checking back is correct after the Jack arrives. Our hand has been demoted to second pair, and we now function primarily as a bluff-catcher.
Easy check back to reach showdown. The Queen is another overcard that further weakens our hand's absolute strength.