Overpair with effective stacks of 2x pot

[Vedocorban]

I'll probably have my own question answered once I read the TMC chapter in PNL (just finished REM), but I'll go ahead and post anyway. Villain is pretty new to the table so no reads.

Ultimate Bet - No Limit Hold'em Cash Game - $0.10/$0.25 Blinds - 4 Players - (LegoPoker Hand History Converter)

SB: $93.29
BB: $78.05
Hero (UTG): $27.35
BTN: $18.57

Preflop: Hero is dealt Q[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/club.gif[/img] (4 Players)
<font color="red">Hero raises to $1.00</font>, <font color="red">BTN raises to $3.35</font>, 2 folds, Hero calls $2.35

Flop: ($7.05) 7[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/heart.gif[/img] (2 Players)
Hero ???

Pot is nearly half of villain's remaining stack at this point. Options are bet/call, bet/fold, check/raise, check/fold. Let's ignore the scenarios where I bet and check and he calls or checks behind.

Is bet/fold or check/fold even an option? If not, do you prefer bet/call or check/raise?