$25NL on Party

BB is ranked as Vanilla/ABC after about 40 hands:

Party Poker No-Limit Hold'em, $ BB (9 handed)

MP2 ($35.22)
Hero ($29.6)
CO ($10.15)
Button ($16.05)
SB ($22.45)
BB ($35.38)
UTG ($14.85)
UTG+1 ($21.39)
MP1 ($22.4)

Preflop: Hero is MP3 with , . SB posts a blind of $0.1.
4 folds, Hero raises to $1, 2 folds, SB (poster) calls $0.90, BB calls $0.75.

Flop: ($3) , , (3 players)
SB checks, BB checks, Hero bets $3, SB folds, BB calls $3.

Turn: ($9) (2 players)
BB checks, Hero bets $5, BB calls $5.

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

Final Pot: $19

Results in white below:
BB has 5c Jc (one pair, jacks).
Hero has Qh As (one pair, queens).
Outcome: Hero wins $19.

I checked on the end, because I just was not sure what he might possibly have. The only real draw out there would have been the straight, which would have made me a loser to every straight draw hand, since he would have either paired his king or made his straight, is this the right play? I find myself checking a lot on the end when my hand is not really that strong, even after I have bet the flop and river.