I don't understand the play here...why are you betting half the pot and then not calling his push?
At least bet 2/3-3/4 pot and then fold if you have a strong sense that you are beat.
Lukie's right about the preflop reraise...3x is standard so 7.50 preflop and then bet/call his allin on this flop.

Your half-pot postflop bet reeks of missed overs - he's likely to have a good pair here and will play back at you given your betting pattern - there's no way to tell whether or not it's AA so I think you have to pay off AA or a set here.
You seem to have gone for a trap play and then given up on it...did you have some read/sense that told you to do so?