NL20 SH QQ vs 1.4 % 3bet

Grabbed by Holdem Manager
NL Holdem $0.20(BB) Replayer
Hero ($48.82)
BB ($42.89)
UTG ($6.31)
UTG+1 ($17.31)
CO ($2.03)
BTN ($15.62)

Dealt to Hero Q♠ Q♦

fold, fold, fold, BTN calls $0.20, Hero raises to $1, fold, BTN raises to $1.80, Hero raises to $3.80, BTN calls $2

FLOP ($7.80) A♣ 3♦ 2♦

Hero bets $16.10, BTN calls $11.82 (AI)

TURN ($31.44) A♣ 3♦ 2♦ K♥

RIVER ($31.44) A♣ 3♦ 2♦ K♥ 3♥

In this popup it show 2% 3bet, so don't know why in my hud its 1.4.

But still - maybe its just a call to setmine after he min3bets? On the other hand I still beat TT, JJ if he has those. By entering even 2% it does not include AK hand, so I can exclude, or its not enought sample?

Preflop I 4bet low to let him show more light, but now I think I coiuld just shove preflop and thats it. THen I still should get calls from TT while on flop maybe he can fold on such boards like this.

On the flop is it worht to bet? I mena - can he call with TT, JJ? Also if we include AK, then we are even in worse situation. Maybe its just c/f