This is just silly. Fat has two meanings. 1)
noun, a type of animal tissue, which serves, as one of its purposes, to store excess energy from consumed food for leaner times. 2)
adjective, describing a person or animal who has a lot of this tissue, possibly to a detrimental level. The first meaning is not derogatory (or shouldn't be), it's just a physiological description of a type of body tissue. It can be in the right places and of the 'right' amount, or it can be in the wrong places and too much or too little. That's when we get into the second meaning (derived from the first) where there is an excess and that excess is getting stored in the wrong places (both on the superficial level and deeper in organs and clogging up arteries & veins).
Thin, short and tall are all just straight adjectives. Them being that doesn't invalidate the double meaning of fat and somehow (by your logic) the word itself.