I like what you did on the preflop and flop.

I don't understand the turn bet. You put him on AQ or small pairs. I don't think he has small pairs because he 4betted pre. You're not getting action from AQ, AJ, or small pairs anyways. You're most likely getting action from hands better than JJ.

I would check and call turn if villain bets < half pot. What's your 4bet calling range in this scenario? Let's say it's roughly QQ, JJ, TT, 99, AK, AQ. I would 5bet pre all in AKs, QQ most of the time. So JJ is in the middle of your range. If you enough evidence that a person is very passive and never bluffs, you could exploitatively fold a turn bet on K high board.

Fold river if another bet comes.

I ponder going all but figure that's too spewey

You have JJ and faced a 4bet pre with JJ, not too happy about it, but haven't you seen enough times at your stakes with garbage?

After villain's check back I put him on AQ oe small pairs so decide to lead

If you target those hands bet a little bit smaller, like half pot

Turn why you put him AQ not QQ? Its microstake 4bet pot. His range will be QQ+ AK. When you betting turn big which hands do you want him to fold. You have JJ maybe the best SD hand. Its easy turn check river fold IMO.

Turn lead is unnecessary as we have SDV plus are capped and behind so many hands. River shove is spewy.