Would love to hear some thoughts on this one.
We are scared of: Ax (AJ A9-A5 A3 A2= 8 combos), QhJh/KhJh/Jh8h. Also Jh9h Kh9h 9h7h. I'd expect 8h7h 9h8h etc. to 3-bet most often.
It looks like I hit everything on the river, so villain is going to fold a lot. It also looks like I don't have that many bluff combos, unless I go crazy with KQ type hand (w/ or w/o ). I would bluff 76s 87s for sure, but I think there's an option to turn SDV into bluff, since it's hard to beat much after villain calls an overbet. QJo w/ J would make a very nice bluff candidate.
Villain called turn quickly and snap checked river, which I thought was odd, so I went for the vbet. I also saw one strange play by villain, and I thought that villain could be bad enough to call very light here, with basically any 2p.
I think it comes down to how often villain calls. I would check vs nits. Interesting spot because both ranges hit that river very often.

NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

CO: 75.4 BB
BTN: 199.52 BB
SB: 203.45 BB
BB: 100 BB
UTG: 81.64 BB
Hero (MP): 115.88 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has T T

fold, Hero raises to 3 BB, fold, fold, fold, BB calls 2 BB

Flop: (6.5 BB, 2 players) A 9 T
BB checks, Hero bets 3.25 BB, BB calls 3.25 BB

Turn: (13 BB, 2 players) 4
BB checks, Hero bets 18 BB, BB calls 18 BB

River: (49 BB, 2 players) Q
BB checks, Hero bets 30 BB,

The river bet is very opponent dependent but against anyone half decent I'd advise against it. Considering your turn range looks like monster draw or monster value it's pretty hard to find many bluffs on this river (maybe you'd turn 3 combos of QJs into a bluff?) and, like you say, villain can have a flush or a straight himself.

It's hard to know what to make of the river sizing.... would you size the nuts the same way? It seems erratic, as if you didn't really have plan if a heart came on the river. It all stems back to the turn overbet. I'd like to hear your thoughts on this but I believe it was a mistake. Villains range isn't strong enough to warrant it and he'll happily fold out all of 9s/Ts/floats/gutshots/even weak aces. AJ and AQ if they're even in his range will consider folding to this turn bet so he only has 99/A9s/AT/A4s/9Ts and monster draws. That's a lot of value to be missing out on. Secondly I don't like it because it leaves you in this no mans land on a lot of rivers (like this one) where you can't get any value from such a strong hand. If you'd bet 2/3-3/4 pot on the turn you could bet the same on the river with a much wider range and get 2 or even 3 streets of value from a lot of hands you'll have folded out on the turn.

Seems fine. Not value betting river is a little nitty. Would prob just bet exploitatively bigger OTF since his range is pretty inelastic for calling. Prob 66%, or more if he's a fish.

Can't imagine checking this back. If you are saying that villain should fold most of his 2 pair combos then you can smash him by just betting can't you? He will have a lot of hands PF after putting the 2bb in, and not many of those are beating you by the river. You'd have to be making lots of assumptions for this not to be a very clear value bet imo.

+1 value bet river. His most likely line is to call with a variety of hands that are weighted heavier towards worse. Can't see him CRB after we triple on this run out.

+1 to betting river. Flop should be bigger. If he's calling anything he's calling a bigger size too.

river looks like slam dunk value bet vs bb's wide range

check tens, check black aces, check nines with no heart.

I would bet smaller on the turn and bet/fold the river. Curious why you chose to overbet the turn.

check piosolver. it's def not a xb but I think you're building two sizes otr and this hand is going in the small size obv.

in vacuum though $30 into $50 is like really telegraphing your hand strength though, innit?

easy bet river all day long, it is not even close