You can never be too rich or too thin, but you certainly can be too gaunt. It means you look skinny like you're sick, not skinny like you have a personal nutritionist slapping your hand when you reach for a bonbon.
A good way to remember gaunt is that it rhymes with haunt, and gaunt people look pale, drawn, and wasted — like you'd expect a haunting ghost to appear. Another way to remember it is that g- + aunt is like great-aunt, and often when you appear to be gaunt you look like you're old — like your Great Aunt Mildred.