every action on the tables should have a reason...it ( a bet) should always try to achieve something...maybe to force oppo to fold (a better hand than yours)...maybe to gather info...maybe to build a pot if you have a good hand or a good draw.
Maybe a good question for you to ask yourself here is " what are you trying to achieve with this bet?" It is doubtful that you bet would make your oppo fold a better hand than yours considering the board....maybe a weak sooted king might fold...K4 diamonds for example if oppo would check call pre with this.
to check here, and to control the pot would get you no info on your opponent's holding. Your bet here achieves the following...it gets info on your oppo's holding...ie you are probably beat.
It is just possible that oppo could hold 2 hearts and is building the pot in case the turn/river hits.
I don't mind your bet here...it will (should) make a lower pair fold, or at least make them pay to draw to a set ...and it makes them pay to draw to the straight or the flush.
I think you were probably beat, and your fold was correct. You can only beat a heart draw or a
bluff.
If you had checked, and the turn was a brick...6 diamonds for example...and oppo had made an 8c bet, what would you have done?
make the note on your oppo's play...move on to the next hand
glgl