It's hard to believe he would check AQ, KQ or a set on the flop as the board is just a bit too connected for that.
Its pretty typical to check your entire range to the preflop aggressor and even more so in this configuration, where there is yet another player left to act behind. If he flopped something really strong, this would be a perfect spot for him to check-raise. He check, preflop aggressor put in the C-bet, hero call in position, and BOOM there he is with a big check-raise.
I would expect QJ, 44 and good flushdraws to play like this a lot of the time, so the fact, he just check-called, makes it somewhat unlikely, he have one of those monsters. But not impossible of course. This is a low stakes cash games, and in these many players are a bit on the passive side.
I honestly dont really know, what bluffs to put him on here, since there are no logical missed draws. Is he turning T9 into a
bluff, because he dont think, it has enough showdown value? Thats kind of advanced, and if so when why not also AJ with the A of hearts. In that case we even lose to some of his bluffs. Maybe he can have trips. I can certainly see a bad player go "LOL I just made 3 of a kind, so I bet". It makes no sense, but if he is bad, he is bad
At the end of the day we are sitting here with a hand, that already build to large a pot. Its difficult to figure out, what is going on, and we are at the rock bottom end of our range. Maybe we can have T9s as a worse hand, but thats about it. So I think, its fine to just let this one go.