is it deragotory...need your help?

Context, proximity between persons, intonation etc convey the real meaning of spoken words. In this question too, if the reply had displayed an attitude of the implied invitation for company for dinner or a resentment to any attempt by the girl to shun the company of the guy citing a different reason, then it would amount to 'derogation'. (Note the spelling).

It depends on the guy's past attitude. If he is usually a jerk, it might be derogatory. If he's usually nice, then probably just a joke. If he's a little of both, then it's harder to determine. I'd also check for tone of voice and facial expression, as well as what he did or said afterwards. I don't need to explain those, as common sense will tell you that a frown on his face in a mean voice is derogatory lol. Even if it was meant to be mean, I wouldn't be offended.

It really depends on the context that he said it in. He could have meant it as an insult or a joke. If he was smiling warmly as he said it, it is probably a joke. If he looked cold or completely serious it may have been an insult. Also are you familiar or do you not really know each other that well? If you're familiar he probably meant it in a fun way, but if you don't really know each other that well it could mean either. If it's bothering you, just ask him! Better to know exactly =]

He may have been trying to be funny, he could have chosen something nicer to say. If you are confused and slightly offended let this person know. But if the two of you are "friends" then he should have known better.

No, I don't think so but it also matters if he said it in a sexual way. He probably just meant for her to eat as much as she wanted, and nothing else.