Only for the view
How could he enjoy weightlessness if he's not free to move? Won't he be attached one way or another? I know someone who volunteered to fly the Zero-G Airbus...He had to be attached and therefore could not float around. He also was not allowed to take drugs against SAS and got sick very quickly.
And let's not forget 0G has a price: 2 or more G's in the way down.
Plenty of people are not allowed for medical reasons to fly the Zero-G planes.
Of course, Hawkings may mainly want to enjoy the view; that's another matter.