What position is V in???
In general in this spot, bottom 2 should be good. Doubtful V limped QQ preflop and we block the 66/77 set making it unlikely.
Since the board is 6
7
Q
it is likely V has K
Q
type hand that we are ahead of.
As far as the claim above that we under-repped our hand. I completely disagree. IN the live game, players don't think so much in terms of pot size, but rather in terms of how the current bet compares to the previous bet. You bet $15 on the flop and then double that on the turn so in the live game that is considered a decent bet. So villain is responding to your strength with strength.
Fortunately, most LLSNL villains will overvalue TPGK hands on FD boards not to mention they tend to overvalue TPGK anyways to begin with. i suspect V is most likely on a combo Q
X
draw. He could also have Q6s or Q7s depending on his tendencies (your profile of V leaves a lot to be desired).
As played, call turn raise with the plan to Value bet all bricked rivers and c/f
rivers depending on V's sizing and tells.