You've got draws, that's why! Any Heart or King will give you a hand. Whenever you have multiple draws like that, start thinking of what would be ideal. If a Heart pops up you have to worry about a higher flush draw, so you probably want the King of Hearts, as he is the most likely to be in someone's hand. A Queen of Hearts would be dangerous for you, since you'd be looking at a royal flush draw vs. a potentially made full house.
Ideally you want a non-Heart King and the straight. That would be the nuts.
For simplicity's sake let's say that in your evaluation, either a flush or straight will give you a winning hand.
You have twelve outs (don't count the King of Hearts twice). That's a little better than a 25% chance of hitting a winning card on the turn. Even re-raising or check-raising would be a good idea in this position based purely on odds. Even if you miss on the turn, it would be in your interests (based on players reactions) to continue to bet it right out.
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