Standard? Overpair goes to flushed river

Villain is 92/4 after 24 hands

PokerStars No-Limit Hold'em, $0.10 BB (9 handed) FTR converter on zerodivide.cx

SB ($9.90)
BB ($9.40)
Hero ($10.65)
UTG+1 ($7.70)
MP1 ($14.75)
MP2 ($11.80)
MP3 ($5.60)
CO ($10)
Button ($7.35)

Preflop: Hero is UTG with K:club:, K:diamond:.
Hero raises to $0.5, 2 folds, MP2 calls $0.50, 5 folds.

Flop: ($1.15) 3:diamond:, 9:diamond:, Q:club: (2 players)
Hero bets $0.8, MP2 calls $0.80.

Turn: ($2.75) 5:heart: (2 players)
Hero bets $2.1, MP2 calls $2.10.

River: ($6.95) T:diamond: (2 players)
Hero checks, MP2 bets $5, Hero folds.

Final Pot: $11.95

Standard. Although I might value bet the river against this tool.

Good point - but, in this case how much would you consider a value bet, where you can dump if raised, but which won't indicate weakness and prompt a reraise from anyone who figures out you weren't drawing to the flush?

$2.50 to $3.00? Doesn't leave you will all that much behind, but at least if you are raised here, you can be confident that you are beat, or at least outplayed by a brave bluffer (not often at this limit).

The problem here is you don't know if you are faced with AQ, QT, QJ, etc. I hate dumping a solid hand on the river to the obvious draw when it's headsup - if you're 3-4 way, you can assume that 1 caller is drawing...but in this case, he could have a set, he could have just 1 pair, or he could have the flush. If I flush someone, I don't tend to bet this much on the river as a value bet...though often enough it's not terrible as it looks like it doesn't want to be called, but does, and probably is called.

wow tough hand to get away from. I think I might call here and probably loose to a flush

I'd tend towards a blocking bet on the river

Maybe you just folded against AQ/KQ or a simple bluff because you showed fear on the river. Yes he might have a flush, or a straight with KJ (he might have 'felt lucky' holding this on the flop and turn).. but I'd definately bet around 1/2 pot on the river to get some information. (blocking bet)

I mean, checking on the river after a "possible flush" hits after raising all the streets before, is just asking for your opp to bluff you out of a better hand.