1) Fold Pre
The flop lead OOP on this board into the BB pre-flop raiser is not necessary. You're only going to get called by better hands. That said, the rest of the hand played out as it would have regardless. Still though, that flop move will put you in bad trouble on most turns and rivers given the action thus far.
I know
@ChipMonster has acknowledged this but yes, this is 100% correct. Let the next BB put in 40% of his stack dark, this is a clear fold pre. I am probably only playing JJ+ AK, AQ maybe AJs in this spot. There are probably arguments to fold everything that's not AA here, tbh.
Now if if you were 2nd in chips but 3rd place was much closer to you, then I see the argument for playing this hand.
2) Check flop.
I don't see any value in donk-betting the flop after the BB was the preflop raiser with second pair middle kicker. An aggressive BB is going to frequently have Ax and Kx here and will continue. He might have smaller pairs you can fold out, but he's going to hit this flop more than a tighter player would that might more pair heavy and fearful of the two overs.
3) Since you made it to the turn...
Then you have no choice, you have just outdrawn most Ax, which I would assume is villain's most likely holding given the action so far. Turns out it's AK, which has you stone dead.
So on the turn I say there is no choice the money has to go in. But I think the two previous streets could have been rethought for sure.