My ex wants me back!!

My ex-boyfriend broke up with me just under a month ago, it wasn't a bad break up because we both weren't happy. I was finally moving on when he messaged me saying it was a big mistake and that he wants me back and has changed! He said he'd do anything to make it work and knows why it didn't work the first time and will change. I wasn't seriously considering it but then he came over and he actually has changed and im so stuck. My family and friends didn't like him and he used to say that if i ever got fat hed break up with me so i was always particular about what i ate . But apart from that he is everything I've wished he could be. But the question still stands....when they say they've changed have they really?