While we can get value from worse hands this board pretty much smashes villain's 3bet calling range which means betting will often put us in a very awkward spot. While I might want to cbet here vs. a very loose passive opponent, checking becomes much better the more competent your opponent is.
As played, even though turn card is far from perfect I feel like you can start value betting safely. The villain had two opportunities to bet already and he declined which tells us something about the strength of his hand. Unfortunatelly, the river is a very bad card and I see no reason to call here.