Most of it is being said. Pre-flop, this is a pretty standard defend against a min-open from the BTN. I don't like 3-betting that much. You're getting way too good odds to play this hand profitably, even OOP. But you'll have to make some plays from time to time and play it more aggressively on the right boards.
On this board however, 7♣:K♥:2♠:: it doesn't make much sense. Button's range is fairly wide here, so he'll be c-betting almost his whole range. Most players will, since it's a K high dry flop making it hard for you to connect on. If you would have a value hand here, like 22 or 77, you're almost never check/raising this flop. So you're not repping any value hands at all.
You only have a backdoor and just check/folding the flop is not all that bad. If you want to make a play, which you will have to do from time to time with such hands, then I'd prefer calling flop and making a play on the turn if any heart hits, or if any 3,4,5,6 hits. Any heart will give you a flush draw, any 3/4 gives you a gutshot and with any 5/6 you can turn your hand into a bluff just in case Villain has the occasional QJo or something like that. By check-raising those boards, let's say:
7♣:K♥:2♠:4♦:
7♣:K♥:2♠:4♠:
7♣:K♥:2♠:5♣:
7♣:K♥:2♠:T♥:
...
You have way more equity here and check/raising just looks so much stronger. If you would hold 77 or 22, you'd always check/raise (or lead) to build up that pot. Also, you want him to charge for your draws. If you turn the FD, every now and then you will hit it as well. Semi-bluffing on the turn is thus way better.
Correct me if I am wrong. This is how I see it. 
