Kjo

If you say he'sgot a high wts, thequestion is what kind of hands he's capable of folding to a turnbet. A8 A7 he certainly won't he may fold AJ ATwith no or you think that's too optimistic too? So cou could barrel J8 JTKTKJ with a flushdraw and i think he could fold this hands but it's not sure. Against an unknown orweak tag i would just try to barrel twice. the turnbet actually doesn't cost you that much with so many outs.

And it'scertainly ok to bet this turn as well as i don't ever seepeople checkraising with initiative on a 3 board so you can't gain immidiate foldequity but when the river is a 8 or 7 , you can get him to fold AT AJ AK and KJ for a split and maybe 44 but you didn't put that in his range. Problem is , that i think, that he could have Ax with Flushdraws as well. 9 is a bard card and you may raise with a pair, with Qx 9x etc.

But as you already have J♥ he can just have A♥K♠ or A♣K♥ or A♠T♥ soo not that many combos with a flushdraw in it but it doesn't really matter. hig equity is just a little higher, checking with K and A♥ but sometimes he'd bet those hands with Overcards and nutflushdraw.

You put the nuts in his handrange. You think he could checkraise those hands? i'd rather expect him be bet/3betting. Checkraise is not good if your hand is strong enough for 3betting and you may suffer a freecard and if you bet turn and river you'll certainly get value from any pair but if you checkraise, it just looks too strong that your opponent may decide to either bet/fold the Turn or not calling another riverbet so checkraise is better with a hand that is not strong enough for 3betting. like KQ.

If he's really that kind of showdownmonkey i think it's not enough just to rely on the hope to catch a straightcard and bluff again on the river but basically it's ok to bet this hand and see how your opponent reacts. Some weakish opponents fold the Turn.