Need help with inspiring my significant other

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So when my boyfriend and I met, we were both pretty big. I was bigger than he was though. He was about 230-240 lbs at 5'7” and I was 256 lbs at 5'5”. He loved me instantly even though I was so big. We both shared a love of food and a desire to lose weight. Even though he is big, he has always been very fit. He is in the Army and has never failed a PT test and he is very muscular. One of the main reasons he wanted to lose weight was so that he could get promoted because at his current size, he can't pass the tape test and thus, cannot get promoted.

Over the past 11 months we have been dating, I have gotten down to 168 lbs (My highest was 270) while he has remained roughly the same size. I love him exactly the way he is. I think he is very sexy. If it were up to me I would cook yummy meals for him all day long. Still, he wants to lose weight. He has days where he feels really ****ty about the way he looks/feels, and expresses a desire to lose weight. He asks me to be supportive and encouraging and I try, but then when he has a bad day where he has cheated on his diet, he gets mad at me when I get on him and tells me to back off.

We are otherwise very happy but I can't seem to get past this schism in his mind of wanting me to push him, and at the same time, to leave him alone about his eating habits. Any advice or tips? He has shown me pictures in the past of him losing large amounts of weight several times, but it seems to always slowly creep back on him. I just can't seem to get him really dialed in this time.