Some background, there are 38 players left out of 1750ish that started, the next jump in money is at 30th.

Party Poker
No Limit Holdem Tournament
Blinds: 8000/16000
(Ante: t400)
9 players
Converter

Stack sizes:
UTG: t844859
UTG+1: t80804
MP1: t134940
MP2: t101039
MP3: t367617
Hero: t203934
Button: t47510
SB: t178892
BB: t91592

Pre-flop: (9 players) Hero is CO with A 9
4 folds, MP3 calls t16000 (pot is t43600). Hero?

MP3 has been fairly loose and raising most of the hands he has been playing. I have been pushing quite a few hands (not crazily, just if it is folded to me with a reasonable hand and less than 10BB), getting from about 100K in chips to 200K without actually going to showdown. The rest of the table (left to act at least) has been playing a ultra-tight get-into-the-money style.

I figure MP3 is slowplaying 5-6% of the time here, the rest of the time he has 22-77, QJs-65s or A8s-A2s with a few other highcard possibilities.

Fold and wait for a better spot, raise to $60K - calling if he reshoves, or shove?

I think shoving is ok. You can add 20% to your stack if they fold. I don't mind folding either.

Ok here's my mathematical analysis of shoving. This is simpler to calculate than raising to $60,000 but I will look at that at the end.

1326 hand combinations.
Button, SB and BB calling all-in hand ranges:
Button: AK-AQ, AA-JJ. SB: AK-AQ, AA-JJ. BB: AK-AQ +AJs, AA-99 (BB is more because he has slightly more invested and is a little short-stacked)
Button: 3.5%, SB: 3.5%, BB: 4%.
Limper: 22-77 - 36 combinations, QJs-65s - 28 combinations, A8s-A2s - 21 combinations, AA-QQ - 15 combinations.
Limper calls us 33% of the time if he calls 50% of the time with small pairs and with nothing else (except the big pairs).
So 56% of the time everyone folds, 33% of the time the limper calls, 11% of the time one of the shorter stacks reraises all-in.
If Limper calls with small pair we are 45% to win. If we win we are +($204,000 + $43,600) or +$248,000 roughly. If we lose we are -$204,000.
45% x +$248,000 = +$112,000
55% x -$204,000 = -$112,000
Total: $0.
If limper calls with AA-QQ we are 28% to win against 12 combinations, 6% to win against 3 combinations. We'll call it 24% to win against 15 combinations.
24%x +$248,000 = +$60,000
76%x -$204,000 = -$155,000
Total: -$95,000.
Discounting the likelihood of QQ somewhat due to the decreased probability of him slowplaying it, there are roughly 12 combinations out of exactly 100 of his limping combinations that are these monster hands.
11% of the time one of the shorter stacks reraises all-in. Generalising, we are about a 24% underdog to the combinations (23% dog to AK-AQ, 28% dog to KK-99, 6% dog to AA).
Ignoring the slight possibility of two players going all-in, against the button we are...
24% x +$90,000 = +$21,500.
76% x -$48,000 = -$36,500
So overall 3.5% x -$15,000 = -$500.
Ignoring the slight possibility of two players going all-in, against the SB we are...
24% x +$215,000 = +$51,500.
76% x -$179,000 = -$136,000
So overall 3.5% x -$84,500 = -$3000.
Ignoring the slight possibility of two players going all-in, against the BB we are...
24% x +$120,000 = +$29,000.
76% x -$91,000 = -$69,000
So overall 4% x -$40,000 = -$1500.

In summary:
12% x -$95,000 = -$11,500 roughly.
56% x +$43,600 = +$24,500 roughly.
21% x $0 = $0.
3.5% x -$15,000 = -$500.
3.5% x -$84,500 = -$3000.
4% x -$40,000 = -$1500.
Total: +$8000.

I think this is a conservative estimate. This is the 300K guarenteed and I don't see many players putting 60% of their stack on the line with a small pair like 44. I reckon with a small pair he will call less than 20% of the time, making this more like +$20,000 every hand. Even if he does call this much, and even if we bump his slowplaying %age from 12% to 20%, shoving is still clearly +EV.

Folding is -$400 (ante), so incorrect technically unless there will be a better spot coming along. The players at the table are about my level, some a little better, some worse. There is $43,600 in dead money on the table, I don't think we'll be seeing too many +$8000-$20,000EV situations again.

Now what about a raise to $60,000? This only affects the calculations in two ways. 1) We probably fold if the SB comes over the top. 2) How does this affect the limper?

It is a better move if he folds more often than if we shove. However, I find this doubtful, given that if we make this medium raise he will be tempted to shove with what he thinks might be fold equity. Against a shove not only does he not have the fold equity, he knows he will be putting 60% of his stack at risk. I can't see how he will be MORE likely to fold against the smaller raise, in fact I think he would be considerably less likely. Of course, we know we are calling if he shoves ($140,000 into $280,000 when we're likely 50/50ing), but he doesn't know that. Either way, we are not getting away from this hand against the limper so shoving seems to me to give us most fold equity, which is the biggest variable in the equation.

I fold here - MP3 has been raising most of the time and limps here to entice a short stacked BB to see a flop? I despise weak aces and I think that raising to 60K which invites calls due to pot odds or folding to a shove is just terrible.

If you're going to play, shove for max FE but I'd fold this. Also, you're third in chips at this table despite your low M so you don't need to make a move yet against a stack that can bust you with a holding like A9o.

Presumably to say fold you've got to disagree with my analysis that shoving is a +$8000 to +$24,000 decision compared to folding which is -$400. As for my standing in the tournament I was slightly below average.

Also, he'd been raising to $35,000 before. If he wanted to induce a shove from me or the small blind, that amount is almost as likely to do it, as it gives us more money to win and a reraise as opposed to a shove he knows would seem to give us more credibilty. But as I said, I've included AA-QQ in my analysis, but just given it a percentage of 12-15%.