What your range reading for the villain on each street? PF, flop, turn, river? Try doing this first.
Any specific stats on the guy that we should know about?

Cheers,

I think checking back the turn for pot control is a good idea here. Your hand doesn't need that much protection and you can improve to a straight. As played I think it's a fold. The board is just a lot more favourable to his range. I can't see much you're beating here.

I think which in this spot we don't have 3 streets of value in a 3-way situation.
I prefer check flop and evaluating turn

Don't mind checking either flop or turn with this hand, the flop smashes their PF calling range and I think you also get often checkraised which is awkward. If villains are aggressive or a bit loose I would take the same line as you did, perhaps betting bigger on the flop and turn and happily getting it in against draws or Tx. As played, I would also fold river if BB seems decent, never folding vs a donkey.