A parallel case (one which seems to be attracting many rulebreakers, unfortunately) is “feels”.
One does not “feel badly” unless one’s tactile neurons are impaired. One “feels bad”.
Every time I hear someone say that they feel badly it makes me feel bad.
To me, and to the Grammar Lady apparantly, “You smell badly” means you are bad at smelling.
To me, and to the Grammar Lady apparantly, “You smell badly” means you are bad at smelling.
What do you make of:
“My room smells badly of cats”.
Hmm… Well I’m not too certain on the correct grammar, but it sounds okay that way. But I think it should be more like, “My room smells bad because of cats.”
Then again, I don’t quite understand how a room can smell bad because “of cats.” Maybe a litter box, but not cats. They don’t smell. Dogs do, but not cats.
That’s different ("…badly of cats"). Now you are again modifying a verb, a complex verb “to smell of cats”. Your room is doing it badly. But grammatically.
Phrase it this way: “My room smells badly ( = stinks intensely) because of the cat litter box.”
If we were Germans we would invent a word something like katgeschmellen. Meinen zimmer katgeschmellt schlecht?