that was a terrible flop for your hand. the straight draws and already made draws are out there and could easily match what your opponent could have.
but he did check, i would then bet which if he called or reraised im gone.
i think your check especially after taking the lead preflop shows me you gave up on the hand already and even a fish would notice that sign then bet the turn no matter what came. so you have to fold the turn.
I would defo continue bet the flop to take it down.

EDIT: i just noticed you raised a EP limp with AJ, do I even need to comment here. i hope you must of had some read on him here.