My opponent in this hand is someone who's game I respect, and who regularly plays quite a bit higher than me. So what's going on in this hand?

Paradise Poker No-Limit Hold'em, $1 BB (4 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero ($365.55)
BB ($365.10)
UTG ($172.90)
Button ($200.80)

Preflop: Hero is SB with Q, K. Hero posts a blind of $1.
1 fold, Button raises to $8.5, Hero (poster) calls $7.50, 1 fold.

Flop: ($19) 4, K, Q (2 players)
Hero checks, Button checks.

Turn: ($19) J (2 players)
Hero bets $12, Button calls $12.

River: ($43) 6 (2 players)
Hero bets $27, Button calls $27.

Final Pot: $97

Results in white below:
Hero has Qc Kc (two pair, kings and queens).
Button has Kh Qd (two pair, kings and queens).
Outcome: Hero wins $48.50. Button wins $48.50.