TPTK against passive opp

[freechus9]

Villain is 53/0 after about 15 hands.

Do I value bet or push?

Paradise Poker No-Limit Hold'em, $0.05 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($15.60)
UTG ($10.02)
UTG+1 ($3.00)
MP1 ($8.51)
MP2 ($6.30)
Hero ($10.00)
CO ($12.70)
Button ($9.45)
SB ($21.22)

Preflop: Hero is MP3 with A, K. SB posts a blind of $0.05.
1 fold, UTG+1? calls $0.10, 2 folds, Hero raises to $0.6, 3 folds, BB calls $0.50, UTG+1? folds.

Flop: ($1.35) 9, K, T (2 players)
BB checks, Hero bets $1, BB calls $1.

Turn: ($3.35) 7 (2 players)
BB checks, Hero bets $2.25, BB calls $2.25.

River: ($7.85) 2 (2 players)
BB checks, Hero...

[Pelion]

15 hands isnt an awful lot to make a judgement but he does seem pretty loose and judging by his play this time i dont think it would be unreasonable to put him on a weaker K here. I think most people would probably have raised 2pair or a set by now so he probbaly had something like KQ or KJ with the straight draw as well. Now he doesnt have the draw to fall back on he might be less inclined to call a big bet so id probably make it $6 or maybe $6.50

The only problem i can see is that it is possible he slowplayed JQ on that flop. If he pushes it will be $6 more to call into a pot of $26 and im not sure thats foldable without a read but I also think youre way behind most of the time he pushes. I think a checkraise is pretty rare on this river though.

[freechus9]

I only have 6.5 left behind at this point, so I think I have to push. That's why I posted this, because I didn't know if I was supposed to v-bet or push, since a push is a reasonable bet on this river.

[mxiu]

Safe push.