NL16 JJ CO vs BB

Flop can be a cbet too. Check is ok.
Turn I don't understand what you mean "valuetowning myself against a K" as you're now losing to any Kx. I'd check back again. You have enough Kx to bet with and other air-balls that should bluff this turn. JJ is not the case.
River ok as played.

Thanks for your opinion. Like it!

I would cbet the flop because of FD present, may be 55% pot, check turn, and then check-back or small bet on river.

I am not really getting 2 streets of value with this hand on this board so I don't mind giving a free card somewhere during this hand. But that's my opinion. About valuetowning I think I suggest that I will lose against Kx. And win against lower pocket pairs. Which is more then 50% of the time if we include some flushdraws as well.

So I lose against Kx and win against his vulnerable showdown hands and win against some flushdraws which I don't pay at all at the river though.

And this is exactly the cause, why I would have delayed the bet once more to the river.

First of all, I would have played the same until turn.

OTT: I would check back. Usually the high card here is a card that I use to bluff if I haven't made a cbet OTF. This means, it is not a very good card for value betting and the reason is obvious. Villian should be scared about the King. If I was villain here, I would think of folding all my pockets and weaker 9s.
You only get value from flush draws. And then again, you could have betted OTF and check behind turn, call river as a bluff catcher.

I think your line was good and I would have betted the river once, like you did on the turn.

Flop can go both ways, depending on your general strategy. I prefer to c-bet my whole range 1/3 pot size, but xb is fine as well.

As played, you have only 1 street of value left after the K comes on the turn. And with J♠:J♣: you block both possible flushdraws hence I would check back turn and make a value bet on the river or call if villain decides to bet. On the other hand if I had J♥:J♦:, I would lean more towards betting 75-80% of the pot on the turn to charge flushdraws and get value from 9x and then check back river.

PS: You could get 2 streets of value if you had c-bet flop, but only 1 after you had checked back. Nothing wrong with flop xb, just saying that as played 1 street of value is due to a bad turn card and the fact you've checked back flop. From flop point of view 2 value streets would be possible.

Cheers