Late position raisers have less credibility than an early position raise generally for having a pair. That would be the only hand you could represent.

Against his stats, he's likely a calling station. Against a calling station you don't want to be c-betting much, especially when trying to represent an overpair. Calling stations almost never put you on an overpair.

That said, c-betting a rainbow flop is never a horrible idea. Board isn't that coordinated, only a possible straight draw.

The turn bet is unnecessary. The J doesn't really change much, it's not really much of a scare card, and any hand he was likely to call the flop with, he's not likely folding to a $1/1.62 bet. If you were to bet $1.50 on the turn, it might serve more of a purpose. I still think giving up on the turn is better here against a likely calling station.

On the turn you had additional outs, but you have to remember you're not a favourite. By betting, you're really hoping more for a fold, the outs are just a backup plan if he does call. So if you're going to bet, bet more and apply more pressure on your opponent.

But again, against a calling station, bluffing, even semi-bluffing is just putting in your money with the worse hand.