Request for deletion, as I'm not seeing the reasoning behind the implication in the first place. Fat is fat, obese is obese. It makes no sense to imply one from the other.
Logically, people would search as follows to find things in an image:
Fat = [ fat ]
Obese = [ obese ]
Either = [ ~fat ~obese ]
Both = [ fat obese ]
By contrast, with that implication in place the required search terms become:
Fat = [ fat -obese ]
Obese = [ obese ]
Either = [ fat ]
Both = (impossible to search for)
... Which really doesn't make any sense.
Updated by SnowWolf