Big time cooler here. You made the raise, in position with the AK. You could have made it 20, but that's irrelevant. At the point that the straddler just flat calls you, OOP, you don't out him on QQ, AA or KK, especially the second two, because usually players will raise you there, to protect their straddle. Overall, you got unlucky and just happened to fall into a bad/mis played pot.
Definitely not a bad beat in my opinion. The way I see it, he was ahead the whole way, including pre-flop. If I was in your position here, I would have had a similar thought process. Eliminated AK since you have it, most likely QQ or TJ. Both scenarios have you beat. When he checks raises on the flop, I would have most likely thought about it, and then made a tough lay down.
You only lost $45 and still have $150, still a decent stack to keep playing with. Usually a aggressive check/raise is sign of a player trying to protect his hand, which is exactly what he was trying to do here.
you got coolered with an unfortunate hand, but I believe you could of laid it down. I am no expert by any means, but I play alot of live 1/2-3 in casinos and one thing I have learned is getting it all in on the flop with 2 pair is normally a losing situation. I have vowed to never call a large all in on the flop unless I have at least a set and the flop is not coordinated. In a higher stakes game an aggressive bluff could be made here by the other party, but in a $200-$300 game if someone shoves it all on the flop or raises big, they usually have the goods from my experience. Just my opinion, but i would have folded the top 2 pair here instead of calling off the rest of my money. So even though it was an unfortunate hand situation I feel you made a bad play by not laying down the 2 pair. Just my opinion.