Curds are a byproduct of milk that has been coagulated. Curds sit in a liquid called whey. Cottage cheese is a mixture of curds and whey. Weigh and whey are homophones. Weigh is a verb, which is the action taken to figure out how heavy something is, which is an action dieters take often. The joke is talking about a cottage cheese diet, hence the clever use of the word weigh replacing whey. 
Cottage cheese diet : eating your curds and weigh .