If villain has AJ we will almost certainly hear about it before the river so I'm not too concerned with that hand. Flushes are a concern but I would expect villain to lead his flushes at least some % of the time given how much check backs we will have on the river.

With these points in mind I push for value here vs his worse Ax. Not sure how we are going to ever consider bet folding given stack sizes? We have under pot left behind so I just jam it in ourselves.

If I've worked it out properly we only have about 1/2 pot left? You've sized it to get it in on the river so I'd just get it in, not much is beating us

Thin value betting is still the best strategy for beating micro stakes and this spot isn't even that thin. You should definitely be betting the river here.