"Thick and tired" is close to the phrase "sick and tired" which means to be thoroughly fed up with something to the point of fatigue. When someone is on a diet, it typically means that they are limiting the amount of food they are eating in order to lose weight, or fat. Thick people are typically chubby people, or people that are considered to have a decent amount of weight on them. 
Diets are for people who are thick and tired of it all .