Being fat does mean you aren't fit. Being thin is necessary but not sufficient for physical fitness.
We can't magically effect the world around us with our thoughts, but it is the thoughts that control the actions we take, so in a very real sense it does need to start from the mind.
Absence of evidence is evidence of absence, especially if you have a cottage industry devoted to looking for evidence, fruitlessly.
You might be interested in reading the old Stoics, who advocated precisely the type of mental control over your own perceptions that you seem to have happened upon.
Marcus Aurelius' Meditations is a good place to start. After that pick up Epictetus and Seneca.