Thanks everyone, there are some good points made in this thread. I'll give a bit more of my thinking through the hand here. Some of it good, some of it... well, meh.
PF - A6o is a terrible hand, I hate it too. That said, these are equally terrible players. When playing live with this kind of implied on the button, I'll make a marginally light call like this to maximize my post-flop playing time with players of this caliber. If you fold it, fine, but the EV of the play is directly and inversely proportional to the post-flop skill of your competitors.
Flop - Were I reading this hand, I'd no doubt also say raise. The key point I left out that Aaron correctly points out is integral, is that I'm regarded as a nit at this table. I've only shown down big hands, and played ABC poker for the better part of an hour. Plus the entire table is fairly passive post-flop if you don't count stupid overbetting of the pot, etc.
Thus, at the time I figured raising this flop would be rather akin to providing the table with a signed affidavit that I have at least an A, and more likely two pair or a set. I also have position on the villain, and I do loves me some position.
So, should I raise the flop? Maybe. It's as dry as can be, and I'd feel pretty dumb if villain folded and tabled two 9s. Remember, I'm a nit, so his bet could even be little more than a position bet. I don't think raising is bad, but given the full context, I feel it's pretty close.
Turn - I have the deck crushed and he checks to me. I'm putting villain on 77-99 at this point, perhaps to my detriment, but you do the best you can. If I check behind, he may bet out defensively on the river, or check/call a river bet from me thinking I'm making a rare bluff. I believe still that, given my table image, checking here is the right play. And I think he checks 33/66 here less than 10% of the time, but that's based on information I didn't have at the time.
River - Villain is a solid regular. There's zero chance he's 3 betting this river with a dry ace against an unknown nit. I also don't think he calls a shove this deep against an unknown nit with a dry ace, but maybe he will some small percentage of the time. So let's examine the possible FH combinations, because that's where I feel we get paid:
A3 - 3 ways
33 - 3 ways
66 - 1 way
A6 - 2 ways
AQ - 3 ways
I'm purposefully discounting QQ to 0 since he never plays that this way.
So I've got 7 win combos, 2 ties, and 3 losers. We can discount some of them based on how the hand played out, but it's still a very obvious shove, as I suspected and you all pointed out. I wish I'd played it that way, but I left money on the table instead with a call and he flipped up A3. Damn.