I personally would check/call the flop too...hits his range much harder than it hits your UTG open range. Turn is tough now given the size but given his aggression so far I think he would pay you off if the flush hits. River you have to fold, pair of queens just isn't good enough here going up against a lot of combos of straights, two pair, and sets. Cant imagine he shows up to the river here with anything worse than two pair, and plenty of J combos in his range to make a straight.

In this particular hand I would have check raised. After that aggression, no use telegraphing my flush and giving him a chance to escape

With as much equity as we flopped I don't see checking as a good idea here.

1) Yes, the board is really coordinated but we still need to remember that we are still facing one pair and draws here more than we are facing big hands.

2) We have a lot of outs here vs. a lot of Villain's calling range. Two overcards vs. pairs that aren't also holding an ace or queen, if one of our opponents flopped a set or straight any heart or Jack can pull us even or ahead. Add the fact that lone Jacks (or even an overly hopeful seven), and worse hearts may be calling a bet here could edge very slightly into light value bet territory.

3) We need to have some bluffs on flops like this, otherwise it's going to become pretty obvious to observant regs that we are only betting here when we have a decent hand so they can either fold worse or call to their draw knowing that they have nice implied odds. If you are going to have a bluff to bet on this kind of flop, this is about as good as it gets (I think that the only better one here would be AhJh).

If it were me, on the flop I would bet if BTN is not known for floating flops and x-r if BTN does like to float. Turn I would x-c since so many combos that call the flop are happy to see that queen. River is a x-f as it happened, if it was a Jack I would x-c expecting to split, on a heart we are figuring out how pot committed Villain as our evaluation for bet size.