1/3NL: Villain's Tentative Call Turns into a Snap Shove; Shall We Bluff-Catch?

It's about dinner time, weekday, local card room. Stacks have been flying all across the table left and right, but it seems to mostly be because the dealer's dealing hot cards and not because I'm at a table of maniacs. I'm the only one consistently on the winning end.

Hero sits on $2k. I've raised 4 or 5 times already this orbit, and it has notably affected the number of cold callers I'm getting and how quickly they're coming along.

Villain (~$260) in this hand has been at the table for an hour, maybe two. He kinda seems like your stereotypical casino rat; late 50s-early 60s, mustache, balding, kevlar jacket, smelled like cigars when he first sat down. The type of person I'd imagine is usually there to bet on the horsies. I haven't seen him before. He's already over-committed to Kings at one point this session and has been way more tilted over a fairly standard spot than the more competent live regs would. I don't expect him to play super predictably, but I'd be surprised if his idea of spew is anything other than over-committing to a pair. Which might make the title of this thread a bit of a head-scratcher ...

OTTH:

Hero is dealt ThTc in EP. Villain limps to us, and we make it $15. 4 players snap call.

The flop ($72) comes Jh 3s 2h. It checks to hero who makes it $45. I could maybe check a street and vbet a blank turn for fatter value, especially since I have the Th redraw, but the players left to act were capable of stabbing at the pot and I expected to get a lot of calls with random pairs and draws.

It folds to villain (we're now HU), who almost folds without much thought. Then, he reconsiders, looks out of the corner of his eye to notice it's me who's betting, and goes into the tank. Nothing about his tank is exaggerated or showy. He doesn't at any point seem to be considering a raise. If he's Hollywooding, then he's doing it with a subtlety that is unprecedented among his demographic. Villain finally puts $45 in the middle and checks dark. For this thread to go anywhere, you'll have to trust my very strong read that villain's first instinct was to fold.

The turn ($162) is the 7s. I make it $54, and villain immediately announces "All-in." I bet the turn figuring his range is pretty much exclusively second pairs, whiffed overs, some 7x gutshots and maybe a smattering of FDs, so I can either string him along a bit more or make him surrender his equity.

It's $153 more to call. Hero fold or calls?