[50NL 6max] Overpair + OESD vs Nit in 3bet Pot

I have been 20/18/2
Villain is 11/9/2.2

Whats my plan for the rest of this hand?

pokerstars Game #19752534595: Hold'em No Limit ($0.25/$0.50) - 2008/08/20 - 00:13:50 (ET)
Table 'Misam III' 6-max Seat #6 is the button
Seat 1: mosess ($105.10 in chips)
Seat 4: No-Fold-Ms.C ($35.70 in chips)
Seat 5: YES. GO ($49.85 in chips)
Seat 6: bw07507 ($50.25 in chips)
mosess: posts small blind $0.25
nihil2501 is disconnected
nihil2501 has timed out while disconnected
nihil2501: is sitting out
No-Fold-Ms.C: posts big blind $0.50
*** HOLE CARDS ***
Dealt to bw07507 [Js Jh]
YES. GO: raises $2 to $2.50
bw07507: raises $5.50 to $8
mosess: folds
No-Fold-Ms.C: folds
YES. GO: calls $5.50
*** FLOP *** [9h Tc 8d]
mosess leaves the table
YES. GO: checks
bw07507: ?

Check behind on the flop = good.

Call turn & river bets barring like aces hitting the board & stuff. Stacking off here on the flop, and we're drawing to 8 outs.

If you're behind here you probably have 10 outs with both oesd and set outs likely good. Against AA or KK you're 38% to win, against a set you're 32%. The only real disaster is if you face QQ (24%) or QJ (8%), but that last hand is quite unlikely.

On the other hand, you are coin-flipping against two-pair hands and crushing AK/AQ hands and underpairs.

Also, given that you're playing 4 handed, I assume villain's range is a somewhat wider than his nitty stats suggest.

If villain's range includes AJ/AT/KJ/QT kind of hands, then I would quite like betting the flop because these are hands that could play along and you crushing them more than makes up for the times you're behind, plus the fold equity when villain has AQ+ and we avoid him sucking out on turn or river.

If villain's range is really tighter, than checking behind is probably best.

The only reason to bet here is to price out AK and AQ, which have 6 and 5 outs, respectively. Since that's not a lot of outs, you might check behind. I don't think you're getting called by worse hands, since he's too nitty to have an open ender.

He's not calling with anything worse and isn't folding anything better. Check for pot control and to see if we can get a showdown.

I'm usually calling a turn bet and giving up if he bets any river since he'll never bet turn&riv without a better hand, basically.