Check calling is certainly an option against some players because obviously we hate it when we get called as we're always behind against someone's range at this point (lots of 2 pairs and flush draws or other straight draws with a better kicker/pair)
Whether we should bet or not depends on villains percentage for folding to flop bets. If he calls a lot we should check but if we make a 2/3rds pot bet (like you did), its fine if he folds a third of the time. (all of those times he will have significant equity since we do not hold a pair)
If villain raises this flop we have to fold since we can be crushed by flush draws with similar side cards.
We're betting any nut flush draw, maybe check calling with medium flush draws + pair, betting overpair and straight draw (KKQJ) and check calling idiot straight draws with small flush (8 :heart:76 :heart:4 )
Our monster hands such as set + flush draw we can go for a check raise or bet third pot/half pot to induce a raise off aggressive players who attack weakness.