Played optimally?

Hey guys. Haven't been around much since school started. I probably only play about 4 hours a week now. Just curious to see if you think this was the right play on this hand. I think its clear villain has Ax and I'm worried about him hitting a higher 2 pair.

FullTiltPoker Game #219256565: Table Monroe (6 max) - $2/$4 - No Limit Hold'em - 14:09:05 ET - 2005/09/15
Seat 1: jeppg1111 ($444.60)
Seat 2: Derek Sabato ($250.30)
Seat 3: andr3w321 ($344)
Seat 4: JooWish622 ($421.40)
Seat 5: BendintheRiver ($348.60)
Seat 6: Mifune ($550.20)
Derek Sabato posts the small blind of $2
andr3w321 posts the big blind of $4
The button is in seat #1
*** HOLE CARDS ***
Dealt to andr3w321 [:As: ]
JooWish622 calls $4
BendintheRiver folds
Mifune folds
jeppg1111 folds
Derek Sabato calls $2
andr3w321 checks
*** FLOP *** [:Ah: ]
Derek Sabato checks
andr3w321 bets $8
JooWish622 raises to $25
Derek Sabato folds
andr3w321 calls $17
*** TURN *** [Ah 3h 6d] [:Kc:]
andr3w321 bets $20
JooWish622 raises to $100
andr3w321 has 15 seconds left to act
andr3w321 raises to $315, and is all in
JooWish622 folds
Uncalled bet of $215 returned to andr3w321
andr3w321 mucks
andr3w321 wins the pot ($259)
*** SUMMARY ***
Total pot $262 | Rake $3
Board: [Ah 3h 6d Kc]
Seat 1: jeppg1111 (button) didn't bet (folded)
Seat 2: Derek Sabato (small blind) folded on the Flop
Seat 3: andr3w321 (big blind) collected ($259), mucked
Seat 4: JooWish622 folded on the Turn
Seat 5: BendintheRiver didn't bet (folded)
Seat 6: Mifune didn't bet (folded)

No raise pre flop makes AK seem unlikely. Your hand is probably best here on the turn. Are you trying to get him to fold with that raise? Or do you hope he's calling with AQ/AJ? I cant decide whether i like the push or if i want to raise to only 200$ and hope he calls with AJ/AQ. 100$ more to call into a 300$ pot is giving him bad odds to draw on a 3 outter to make a bigger two pair. And if you are already behind he's just going to call your push.

Edit: Forgot he would be getting 3 more outs from possibly having the board pair the king on the river. But even still 6 outs out of 46 card(45 if you say he's holding one of the other aces ) is still a bad draw for an extra 100$.