Being german, the first thing that came to my mind was 'He cares for his corpse' , because of the german word 'Leichnam' But that just would be a bit too creepy ^^'
what would be "he worries for his body?"... I don't understand the difference between zorgen voor and verzorgen...
"He worries about his body" would be "hij maakt zich zorgen om zijn lichaam".
"Zorgen voor" and "verzorgen" are pretty much interchangeable.
It doesn't really mean the same thing as looking after your body. You can take care of your body while still being a workaholic, for instance.