Fold or no fold? What to do???

The proverbial smoking gun...

Okay - here's a real stone cold whodunnit...  We're deep stacked at a $.25/.50 table today - $80.20 is the effective stack size (I'm sitting on $145.05).  I don't have any real data on my opponent.

I look down at AsQd from the CO and open for a standard $1.50.  I get called by the SB.

$3.50 in the middle, flop is 5s7h3s.  He's got a wide range, but this kind of flop mostly misses any strength save for the obvious sets.  However, I want to charge for any draws he may have.  I cbet for $2.50 and he calls.  No timing tells or anything; he pauses and check raises me for essentially a min raise: $6.75.  With a backdoor flush draw and 2 overs, I call.

$17 in a growing pot, we see our bingo Ad.  Our opponent continues his aggression, though betting a bit on the small side after his flop c/r: $8.50.  I think I call here - I don't see what raising accomplishes; I keep in all his bluffs and open myself up to be jammed on (which I probably have to fold).

River is a 2rd A: Ah.  $34 in the middle.  Final board 5s7h3sAdAh.  I hold trips.  He open jams $63.45 into the $34 pot.  WTF?  Let's play this back: 64 is possible, XsXs - (As6s, As4s are not possible since I hold the As), set of 5's, 7's or 3's.  Does a naked straight draw play it this way (i.e. 6sX)?  This is so far out of the realm of the player base - I have yet to see this kind of action and pressure from this pool.

What do you do here?

I folded - given the action, there's simply too many hands that beat me that act like this the whole way through.  His hands are so slanted towards value with the rivered boat...

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The hand in question is linked here.