If this man was boarded last, then Southwest was well aware that the plane was full, and that there was only one seat left, and that one seat would not work for this fellow. That is why I would hold SW partially responsible. The "big guy" may not have been aware that there was only one seat left. Even if there were just 2 left, people on the plane would probably shifted around to let him use 2 seats.
However, if it was me as the bigger person, I would have known I needed 2 seats, and even asked SW as I boarded, if there were 2 seats available for me. If they said no, only one seat, I would not have gotten on that plane. And I would way rather pay for 2 seats, or ask for 2 seats, than spill over onto other people. (I am not thin, but fit inside my seat fine on planes, so I have sympathy for the overweight).
Sorry this situation had to impact your trip, OP.