Saturday night playing $1/$3 at the casino 8-handed. Table seems somewhat loose passive.

Hero is dealt 2c 2s on BTN with $300 stack.
Folds to me (very rare on this table)
I raise to $15
SB folds
BB calls $15

Flop ($28, HU) is Jh Th 4h
BB checks
Hero Cbets $20
BB calls $20

Turn ($64, HU) is 9h
BB checks
Hero bets $45

What are your thoughts on everything up until this point (I'll tell you what happens afterwards)?

JhTh flops arent great flops to cbet, but depending on villan and playstyle you can cbet 100% IP HU, so no issues there, bet sizing is right both pre and on the flop.

Turn bet is spot on. Third barrel when 4th heart comes and he checks sounds solid, well played.

I used to always raise here. I now think open limping is probably better. I'm unsure.

I cbet smaller. Villain is very rarely going to be able to continue here, so let's just get this done for as cheap as possible.

I'd probably check back the turn and take my showdown value (noting that we do have showdown value against pairs, two pair, KQ, etc.). All betting does is perhaps get small but better flush draws to fold, but that only makes up a portion of his range.

Our hand is too good to bluff, imo.

ETA: Whoops, thought we had the 2 of flush. I like the bluff a lot more now as it likely folds out a huge amount of hands that can't call (but are better). If called, we might have to triple barrel the river to get two pair / stubborn straights to fold.

GcluelessNLnoobG

this is really just a range question.
He's almost certainly folding all 2p and worse hands.
And calling with all sets or better.

So what was his range pre flop?
If he plays a lot of unsited cards, then I suspect this is bad (esp on the flop) given that he has a ton of 1 broadway flushes now.