Well, I think I would make that same raise on the flop to 0.45$, and the exact amount. However once Villain did a 3bet, I wouldn't re-raise here.
I don't think you can get called by a worse hand, but only by better ones.
Basically, you are hoping opponent has nut flush draw that he might call/jam with in which case you are hoping TP survives, everything else that calls/jams has you beat, and weaker hands would be chased off. Considering there are 4 hearts out there already, it is hard for V to have any flush draw, making his range even tighter when he 3-bets you.
Raising the flop is fine. In a BvB spot like this, you want to be raising a pretty wide range if you're playing against someone a lot. You said you have no history, so I don't hate just calling. But in general, w/ TP + draw hand in BvB raising here is generally +EV.
I would like to know, would you have played this hand the exact way hero played it? If not, what would you change?