Thank you all for the feedback. After further thought and discussion, I can see the merits of both plays (call or fold), but I strongly disagree with the primary justification for calling.
Most posters advocating calling are using the justification that this is 10NL and we are playing for dimes. The level you are playing is not an adequate reason to call off a stack. While I will admit that most 10NL players (myself included, that's why I am a member of the forum) are bad players, I will not accept that they are dumb, as all poker players deserve more respect than that until proven otherwise. Also, another thing to consider is that the Villian acts second, not first, postflop. Had they acted first, I feel a fold would have been too tight based on the information I had. Acting second, it's much closer.
In my experience, 10NL players make many mistakes, but they tend to be mistakes of passivity (checks when bets are better, calls when raises/folds are better), not aggression. Most players and games are passive, so my initial assumption about all unknown players at this level is they are passive. If you find a player being aggressive, they tend to be polarized: either a maniac who is splashing around a lot, or a nit with strong holdings. Because most players at this level are recreational, and hate to lose money (and hands), the aggressive players tend to be weighted toward the nittier side. Since the player was unknown, I would like to go through a quick rundown of player types, and see which ones I could beat based on the action.
Maniac: A call is justified here and will probably be best, as they could be bullying and their hand range is very wide. However, my opponent has been too quiet through the first 15 hands to be one, so we can rule this one out.
Good LAG: No way I am beating a good LAG, as they would read my 3-bet PF and c-bet as strong and would not be shoving a rag board trying to get me to fold AK, since 10NL players don't let that hand go on this board. Good LAGs shove for value in this spot, expecting to get called by worse. A bluff from this player would tend to be smaller, trying to look like a "keep 'em in" value bet. Think min-raise.
Bad LAG: It's possible a call would be good, as they aren't as skilled and tend to try to bully more, but not to the level of a maniac.
Good TAG: Not likely. A good TAG isn't shoving 7x with many bluffs. I could possibly cooler TT (which I don't think shoves here-most likely raises something that could extract value from worse hands). Also, good TAGs won't be shoving a full stack on the flop often.
TAGfish, Tight-Passive, Nit, Loose-Passive, Calling Station, Fish: No chance in hell! While we all consider these guys to be the bread and butter of money in poker, by definition, they tend to be passive and only make aggressive actions when they are certain they have the best hand. Some could argue these players will show up with TT-77 here, but I would expect these players to be afraid of me holding overcards and "sucking out" once all the chips are in the middle. Plus, because I 3-bet (putting AA-QQ in my range), these players shoving with those hands becomes more unlikely.
Now some may say that these players will call the PF raise with a wide range, including connectors like 54o and 75o, to which I say, yes you are right. But when 10NL players do this, they are typically playing fit-or-fold, not bluff 'em out. So, considering the action, which of these extra hands shove? I'm guessing 87-32, all of them +EV for Villian in this spot, since 76 and 43 are pair+OESD combos (13 outs twice) even though I am currently beating them. Fish will overplay draws, but on the flop, it can often be profitable to do so at 8+ outs if you get stacks in the middle, and if something is profitable for your opponent in a HU pot, the profit comes from you. The Villian possibly shoves some of the two-gappers (particularly 64, with 75 and 53 being possible as well).
So, Villian's shoving range (at widest) is QQ-44 (expect AA, KK, AK to shove PF), 87-32, 86-42, and at most AQ as a pure bluff (which I rarely expect at 10NL) for a total of 187 combos, broken down as follows:
Straights: 32 combos, my equity = ~0%, needs runner-runner
Sets: 9, equity = 8%
Two Pair: 24, equity = 8%
Overpair: 6, equity = 8%
Underpair: 24, equity = 92%
Pair+OESD: 48, equity = 52%
Pair+Gutshot: 24, equity = 66%
Bluff: 16, equity = 75%
Equal Pair: 1, equity = 50%
This gives a total equity against the widest possible shoving range of ~42% for JJ. Pot Odds
= 11.59:7.41, remembering that Villian has me covered, so I need at least 40% equity. Mathematically, it's a thin edge that vanishes completely if Villian does not have the AQ combos in the range (Equity = 39% without AQ) and gets smaller as hands are removed from this range, starting with the weak pair gutshot combos. From this analysis, it is a close call at best with high variance to a fairly easy fold. I would also argue that, at 10NL, folding is most likely the exploitative play that saves you money and limits Villian's profit.
The big take-home here is that at 10NL, insta-calling this shove because Villian could have TT or lower AND puts you on AK/AQ will deplete a bankroll quickly and it could point to a leak in your game. Just a warning to be careful with that thought process because it is dangerous to cap your opponent's range to only hands you beat without the nuts.