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We could really do with more information here. How many players were at your table and which positions were you and villain in? A 3BB open-raise from UTG should usually be treated differently to an open from later positions. Also how many hands have you played in the game so far and do you have any read on villain? How often does he open raise? These questions and more help you build an idea of the range of cards villain might have.
We also need to know the size of the pot, If you or villain were in either blind the pot will be different than if both blinds folded pre-flop.
As hero played we gain very little information on villain through the hand. He liked his hand pre-flop and c-bet the fairly wet flop so probably still likes it. On the flop you may have the best hand and you have lots of outs to what is probably the best hand, so I would consider re-raising to roughly 2.5-3x villain's bet. You may make villain fold, a good result with K-high and he if he calls I would probably fold the turn if villain bet (and I didn't hit my draw) or check behind, getting another chance to hit a draw.
As played I would say hero is probably behind to a better made hand and is not getting the correct odds to call, despite his many outs, so has to fold.
Edit: with no read on villain or certain extra info (villain is tight and UTG, for example), and if hero folds to the turn bet, then I don't mind how hero played. He had a playable hand pre-flop, probably had the equity to call the flop bet and managed to keep the pot small throughout, losing a small amount when it would have been easy to lose a lot to a disguised hand.
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