As some people pointed out, there's some information missing. Villain was playing at the big blind position?
It seems that you did not raise pre-flop, so that's first mistake I'd say.
Given that you didn't raise pre-flop, villain might not think you have KK or AA, think yourself if you're villain, if you had top pair, your opponent didn't raise pre-flop, would you fold here? Probably not as the board is not very coordinated either. When you bet $3.50 on the turn, villain still might be thinking you had a 10. In heads-up play, having top pair is usually very strong, and you haven't really shown him any real strength to fold his top pair.
Of course the river Q is a bummer for you, but even so, I think the game would've been different if you raised pre-plop.
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Ok, now let's see a flop!
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