First of all the preflop play was the right one, should be clear.
Villain just did a call, which is pretty likely from the BB.
So I would say that the premium hands are not in his range.
The only premium hand which he may just call and not raise there is probably A K suited but i think he would re-raise this too.
You hit the Flop really good and i would say you are way ahead here.
There are only three hands which would crush you , J J , A J and A K but for a TAG this hands would be standard re-raises pre-flop (Maybe not A J)
You did a value bet on the flop which is obviously right. But i would say you should have bet higher there like 3/4 or pot size because an A X would call you anyway and the other opportunity would be a Flush Draw. Something like Kh Jh or Qh Jh.
A Flush Draw has 9 outs (9-1 out because of your Queen = 8 real outs) which is a chance of 32% that it comes within turn and river. You bet 50% of the pot and even if a call with that draw is -EV there the most player on this stakes will do that. And guess what? They will do it even with 3/4 or a pot size bet. And in the end you will have more profit from that in a longterm.
Yes, sometimes they will fold there but you will win more money with a larger bet in this spot.
I would say the turn is a blank because 99 would have folded on that Flop after your Cbet and it would in the most cases be a reraise pre flop from a TAg when you are heads-up and he has position.
The Check was a fault, i know you want to slowplay him I did this mistake in my early stages too.
But why should he fold to a bet when he called your bet on the flop?
Lets still say he has his Flush Draw in most cases he would say thank you and take the free card. But he raises, why?
It is likely that he has one J and in many cases combined with a Flush Draw.
He will think now: "Oh well it was just a Cbet from him and he has total air, i will grab it now."
His Bet size looks like a value bet or a bet to get you out of it. It can be seen in both ways (value bet because he thinks he is ahead with a pair of Jacks).
That you re-raise it was the right decision but again way to small. Why a min-raise there? You are probably way ahead and it is very cheap now for a Flush Draw just to call it again. Lets say he has Qh 10h then he gets an open-ender on the turn too and more outs.
The River is a bad card for you. The Flush Draw gets along and if he hold Q 10 he now has his straight.
Even if you have lost there it his hard to fold this hand if you check and the villain bets. A good option there would be an easy check-call.
Many people will still think they are ahead there but how the villain play his hand looks like he won it on the river.
The main mistakes here are the bet sizes on flop and turn and the check on the turn.
I can understand that you dont want to scare the villain out of the pot on flop and turn but going for full value with large bets is on this stakes the best option even if it seems like they are always folding when the flop is with you.
I would appreciate it, if you can tell us how the hand ends.