Villain is a reg running 22/17 and 3 betting 8.5% and plays more of a 3bet game from BB than flatting even against EP raises

Pre seems standard but flop I'm really on the fence. I definitely think he can check some better pairs with a heart as well as hands like AK/AQ with a heart as well as some give ups. Think he mainly check folds with over cards without a heart so I dont think we get value from anything except A high hands. Is there any merit to betting flop for protection or should having a heart make us more inclined to just check back and bet with pairs without a heart?

Turn I was confused by his lead as did not expect he would have many 7x hands and we do pick up more outs against his over pairs. After looking through some reasonable ranges though I think we should just fold considering its dificult to evaluate whether any of our outs are clean and not many pure bluffs in villains range when he takes this line.