I prefer the re-pop on the flop. How many times does he have 44 or K4 here? I understand the call though...
Hands that beat you...
KT - Very possible
44 - Possible
K4 - Unlikely
Hands you beat that he might make this bet with
34 - Plausible

- Plausible
KQ, KJ - Have to be considered as possible but I dunno with the preflop action
I dunno man this is so borderline...
What's more likely the top 3 or the bottom 4? I'd argue they are quite close. I'd use all the timebank that's for sure. The hearts are kind of irrelevant apart from to define his hand. 60:40 in favour of folding here...