in addition to the usual recommendation about a physician’s clearance and things like that, my main advice to you is to recognize that the excess weight is HIS problem, not yours.
He has come to you seeking help, and that is a good step but having a trainer alone will not help him lose 100 lbs. Unless he gets his eating under control, his weight will stay right where it is, particularly since you also write that he lacks motivation, is under stress and very busy. I hate to say it but hiring you as a trainer may be nothing more than a fig leaf.
However, having said all that, you can still do a lot of good here. Even if his weight does not budge, exercising will improve things for him. At 100 extra pounds, there is a good chance that he is on medication for hypertension and is diabetic or on his way, and exercise can help regulate some of this. He may also have some joint issues like knee and lower back pain, and getting stronger can help manage this as well.
If you are lucky, you may be able to jump start the motivation that he is lacking by your description. His perceived lack of motivation may be a feeling of being overwhelmed at the thought of so much excess weight, and seeing some improvement could be the light that he can suddenly see at the end of a tunnel.
A situation like this is tough to manage. As trainers, we want to help so much and take it on as our responsibility. But, ultimately, it is not. If you can even just keep him exercising, you can pat yourself on the back even if he never will be a poster child for a ‘before and after’ success story.
I wish you good luck.