Live Casino, NLHE $5/10 Blinds, Full Ring, 10 Players

PREFLOP:
Hero UTG raises to 30 with Ad Qd.
UTG2 calls 30.
LJ calls 30.
BTN calls 30.

FLOP: 9d 4d 2d (120)
Hero UTG checks. UTG2 checks. LJ checks.
BTN bets 80.
Hero calls 80.
2 folds.

TURN: Kc (280)
Hero checks.
BTN bets 150.
Hero raises to 420.
BTN calls 420.

RIVER: Kh (1120)
Hero checks.
BTN bets 700 and is all in.
Hero ????


**Villain is a reg that is quite LAGGY but opens quite light preflop with JTo in MP and may also limp call J7s in EP facing a preflop raise.
**Hero flops the nut flush as the UTG preflop raiser. Hero decides to slow play and just x/c flop and plan to x/r turn. Then river pairs the board.


Questions:
1) How is the bet sizing on the turn check raise?
2) The board pairs on the river. Can you value shove the river given the sizes or just bet half pot or just check an decide on the river? I think Villain has 22 or 44 or K9s here quite often as his turn continuing range after Hero x/r are only sets, 2pair and lower made flushes. Hero already has the nut flush made on the flop.

Can I ask where this is i.e casino/location? not entirely sure I love the ch/call on the flop but w/e... From what I can tell were to shallow to be genuinely be considering folding this hand at any point especially against described villain. As played call river! but, I would much prefer to just shove ourselves & rather be check/eval if we had a medium flush but since we have the Ahigh flush his bet/calling range OTT should consist of Kx all sets and all smaller flushes.

Unless you have a very low SPR, I don't like checking this flop. You aren't looking for someone to "bluff" at you, you are looking for someone who also flopped well to give you action. People tend to play their sets, overpairs + fd's, and lower flushes pretty fast on these sorts of flops, so I would absolutely bet the flop. I think you were looking to get too fancy on this hand.

I would've preferred you shove the river, but now that you checked and he went ahead and bet for you, it's a pretty obvious call.