Now this looks rly retarded... but it seems like the only way to play the hand ♦ 
$0.50/$1 No Limit Holdem
10 Players
Hand Conversion Powered by weaktight.com
Stacks:
UTG ($32.38) 32bb
UTG+1 ($111.65) 112bb
UTG+2 ($100) 100bb
MP1 ($104.65) 105bb
MP2 ($102.15) 102bb
MP3 ($50.88) 51bb
CO ($169.33) 169bb
BTN ($63.51) 64bb
SB ($24.58) 25bb
Hero (BB) ($127.83) 128bb
Pre-Flop: ($1.50, 10 players) Hero is BB Q♥ Q♣
5 folds, MP3 raises to $2.62, 3 folds, Hero calls $1.62
Flop: 4♠ 2♠ J♣ ($5.74, 2 players)
Hero checks, MP3 bets $2.87, Hero folds
Final Pot: $8.61
MP3 wins $8.33 (net +$2.84)
Hero lost $2.62
At first I was like weee QQ in LP vs a 40/x fish!!!! But when I take a closer look at his stats, I see that he's 40/1 over a 1,2k sample, with 0% ATS with CO % BU each being 1% PFR (fwiw KK+=0,9%). I guess you can argue the sample is too small? but come on, no stealattempt at all in 1,2k hands? (as im typing this, handcount is up to 1,3k and still 0 ♦)
setmine and c/f ftw