Going to respectfully disagree with the above.
Certainly some weak players will call because they do not have the nerve to push and their hand is too good to fold, and then give up when another barrel comes. Good players can often smell that and exploit it.
This is true in some situations but this is not one of them. We are being asked to put one third of our stack into the pot on the flop. It is not realistic to expect him to give up on the turn that often especially after the super strong donk bet. If we call on the flop then we are expecting a shove on the turn and we should be snapping it off as we are basically putting him on a smaller overpair. As far as some players calling because they do not have the nerve to shove, calling is a better play than shoving in this spot. Also it smells nothing like weakness to me, more like the opposite not a spot to try and exploit.
However I think it is quite a legitimate option, in position, to pay for another street and re-evaluate based on the extra information. The float shows strength, and a lot of players would shut down in BB"s spot here if they do not have it. It is clear from the post that he studied the BB carefully, and felt there was now enough evidence of strength to get away, with a decent fighting stack.
The evidence was the same on the flop, what we expected to happen has happened. We should be calling IF we call on the flop (which I don"t think we should). We should only be calling the flop to call the turn and NEVER EVER fold no matter what the turn is.