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This is fine.

After the Turn raise you should stop being aggressive. You are probably behind now, ut the pot is big enough to warrant a call down.

For the record, had he Capped the Flop, Just call down.

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As a side note, let's say you were the other player and you had KK. Do you 4 bet the flop or just call letting the other player take the lead knowing that he will most likely lead out on the turn so you can 2 bet him there. I struggle with these situations a lot because I am thinking I'll give up 1 small bet now when I am way ahead so that I can trap the other player for 2-4 big bets on the turn. Is this really bad thinking here?