Are sure thick doesn't equal fat? I mean, let's look at some actual definitions of fat:
of a person or animal) having a large amount of excess flesh. (First result on google)
: notable for having an unusual amount of fat:
a : plump
b : obese
1. Having much or too much fat or flesh; plump or obese. (The free dictionary)
1 a person or animal that is fat has too much flesh on their body and weighs too much. It is not polite to call someone fat
having a lot of flesh on the body:
The definition of fat is plump, obese or containing grease or oil. (Yourdictionary)
having a lot of extra flesh on your body : having a lot of body fat (Learningdictionary)
And here's some definitions of plump, because the word shows up so much.
having a full rounded shape.
slightly fat. (First result on google)
well filled out or rounded in form; somewhat fleshy or fat. (Dictionary.com
slightly fat, in a pleasant way. This word is often used to avoid saying fat, which is not considered polite
Well-rounded and full in form; chubby