It doesn't sound like you can do anything else than what you have already done.

He is in denial. Plain and simple. If he swears that he is following the diet and yet ordering Dr Pepper and eating bread, well.....I don't know what to tell you.

It isn't your fault. Other than next time he says "I am gaining weight your diet sucks" to simply state, where in the book does it say you can take a bite of bread and drink a large Dr Pepper? The diet does work but not if you continue to eat stuff not listed on those 4 pages of induction so it's YOUR fault not the diet.

You are not his keeper. He has to follow the diet for himself, you can not force him. He has to want to lose weight and follow the plan.