re: Poker & when to let go of three bet
It's not really a tough spot to be. Since he just flat your 3-bet preflop, it's unlikely he would have JJ+. If he was set mining and flopped 4s full of 7s, I doubt he would be raising, as it could scare you and cost him some value on later streets. Sure this flop fits best his range (flatting 3-bet on the button, looks like suited connector or small PP) than yours, but I don't see anyone with a monster and in position NOT slowplaying this hand. I imagine that if he was holding a strong pair, like QQ+, and he was going for a trap, he would keep his trapping strategy and keep slowplaying his big hand.
I would be pretty comfortable after some thought, of shoving any raise. A 4-bet on the flop looks doesn't make any sense, unless he's holding 56s or 66-22, minus 44. Since he folded to a C-Bet, I'd put him on a weak ace, or a KT, KJ or a 89s-KQs suited connector hand. No reason to freak out to a 4-bet, but I understand that poor players can make you confused and induce a mistake.
In this case, raising with a monster is really a bad play and can confuse you. But I tend to think even worst players understand the benefits of slowplaying monsters. If he is a good player, he would know that you could be 3-betting blind vs button with any two cards. One more reason for him to slowplay his monster/try to bluff or semi-bluff the flop. Anyways, this leads to the only conclusion: SHOVE. Three possible scenarios: 1 - he folds his bluff/semi-bluff; 2 - he chases his draw and lose a high percentage of times; 3 - he calls and shows his monster. You say nice hand and take notes, you'll probably play him again in this very same sit and go since you got him covered. Imo, neither are negative scenarios, as you kept alive.
I'd be more scared if he called in this dry board, if you ask me. Of course I'm never folding here, unless some big ace, king, 8 or 3, flush show up.