3 bet pot line check?

Played a hand yesterday in a 3 bet pot with JJ from the small blind. Preflop got called by a late position raiser. Flop came 9 high, two clubs, I c-bet and they just flat called. Turn was a low card, didn't complete the draw. I slowed down and checked, they checked back. River was another blank and I ended up firing again. They tank called with 88 and it got me thinking if my check on the turn just gave up too much info, or if betting three streets is just torching money with a hand like JJ.

I usually stick to roulette or blackjack but I'm trying to make poker more of a regular rotation. Figured I'd get some input on whether the turn check looks weak here, or if there's another line I should try. When do you keep betting these spots, especially out of position?