Also not likely that the plane was overweight. With only the pilot and full fuel the plane was well below takeoff max weight. True that many if not most 4 seat planes will be overweight with 4 occupants and full fuel what is normally done is the plane takes off with less than a full tank of fuel to be under weight limits.
It appears this crash was because of mechanical problems, he aborted his 1st takeoff after getting only a few feet off the ground and told ATC that he had problems and was going back to the hanger. He returned about 15 minutes later for the fatal takeoff wrongly believing he had the problem resolved.
Correct you are on each point but I was not trying to diagnose this accidents fault, just answering the question asked, in this day how can this happen, LOTS OF WAYS.