$10 NLHE 6-max: Standard line check hand w/ KK

No reads on villian. Should probably have raised the turn though because it's pretty drawy and I think a lot worse is going to call (something I learnt a few days ago .. after I played this hand).
Flatting the river after some draws missed and he could also be vbing Jx?
BB: $10.53
Hero (UTG): $10.49
MP: $4.23
CO: $10.25
BTN: $10.40
SB: $11.00

Pre Flop: ($0.15) Hero is UTG with K♥ K♠
Hero raises to $0.30, 3 folds, SB calls $0.25, 1 fold

Flop: ($0.70) J♦ 4♣ 5♣ (2 players)
SB checks, Hero bets $0.50, SB calls $0.50

Turn: ($1.70) 8♣ (2 players)
SB bets $1.08, Hero calls $1.08

River: ($3.86) A♦ (2 players)
SB bets $2, Hero calls $2

jbbb said:

Flatting the river after some draws missed and he could also be vbing Jx?

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Just raise the turn, then the river is a lot easier to play.

why raise the turn?

Looks fine to me as played

bgomez89 said:

why raise the turn?

Looks fine to me as played

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Well I think a lot of draws can be betting small on this turn for a cheap river. If we raise now we allow him to make calling mistakes with draws or Jx. However if we call here we can allow him to play almost perfectly on the river if he hits his draw or bricks so there is less chance of him making a calling mistake OTR.
hands that might be this turn 9x, Tx with one club, a4, a5 w/ ace of clubs Jx with j of clubs etc. I don't see a lot of made hands wanting to bet here.

Is my thought process going in the right direction?