PokerStars $3r - TT: Push, fold, or stop-and-go?

[LCposter]

Results: Hero pushed pre-flop, villian called and showed KK, no miracle T for hero.

Villian's 4xBB raise turned out to be KK for the second time, but I don't know if I can put enough stock into the bet size to find a fold here. My thinking is that with a below-average stack, only ~14 BB, and knowing the pot will be heads up, I have to go with TT unless I read villian as being JJ+ at least 50% of the time.

Agree or disagree?