Opp is a semi-loose donk, the type who takes toppair hands too far (in the passive way by calling down). I had seen him call an allin on the flop with TPTK before (he was close to folding though).

Party Poker No-Limit Hold'em, $ BB (5 handed) FTR converter on zerodivide.cx

UTG ($30.94)
MP ($25.05)
Button ($21.10)
Hero ($70.82)
BB ($47.81)

Preflop: Hero is SB with K, K. Hero posts a blind of $0.10.
2 folds, Button calls $0.25, Hero (poster) raises to $0.9, BB calls $0.75, Button calls $0.75.

Flop: ($3) 2, 5, J (3 players)
Hero bets $2, BB raises to $4, Button folds, Hero raises to $8, BB calls $4.

Turn: ($19) 6 (2 players)
Hero checks, BB checks.

River: ($19) 2 (2 players)
Hero bets $10, BB calls $10.

Final Pot: $39

I lead the flop for 2/3 pot, and when I get minreraised I'm getting a little suspicious, but his minraise could very well just mean toppair (a lot of fish minreraise the flop with toppair). I reraise him hoping for a call from a J and I will fold if he comes over the top of me (note: I should probably reraise a little more).
He calls, and I think there's a good chance he has the J and not a weird twopair or a set. I dont want to bet because (1) I might still be up against twopair/set, and (2) a weak J might fold the turn with that much strength shown by me - so I check to induce a bet from him. He checks behind, and I'm pretty sure I have the best hand by now. Also the 2nd 2 falls on the river, a card that might counterfeit a possible weird twopair hand. I think I have the best on the river more than 70-80% of the time here and I make a ½pot valuebet.

Hows my thinking on each street?