I would think a lot of Jx hands would call pre-flop instead of raising, especially after one person called $15. AxQx is possible as well, but you block aces. i would also think that other Qx hands would call as well. I do agree that you underrep'd your hand by calling the $35. At the end of it all, I'm thinking what V may have put you on is AK suited. So without thinking much of it, he kept betting out to hopefully take it down.
From V's bet sizing on the flop and the turn, he kept pricing you in to call (which considering he had 99, he has to know that he needs to turn his hand into a bluff right from the flop). If he wanted to represent a J, he would have checked the flop (which you see a lot of people do in these stakes... so they can have the other person bet into you). Since the 8 would essentially be a brick, you may have bet, V would jam all-in, and put you in a tougher spot.
Considering the line villain took, I actually believe you made the right call.