This question is so removed from reality as to be almost useless.
I think, however, it is the height of social thought police autocracy to brand someone vain for saying no.
The implications behind it are far too vast. Why only one life? Why do you only save one guy? Is there a limit it would stop being ok? 75lbs is ok, but 150 not?
Is the only stopping point meant to be the point at which it would kill you? In which case, the implication is that everyone should sacrifice everything they have to save other people's lives until you can sacrifice no more.
When people who ask this question give away all their money and possessions to people that need it more in the Third World, THEN I will believe there is a possibly superior morality behind this question. But you don't, do you, even though that money will save lives, whereas you live in a comfy western world abode free of cholera and hunger. This situatioin is real, not weirdly hypothetical like the given question, but it deals with the same concept- yet people feel they have a right to their money, even though they are living in relative luxury whilst others starve. Fact is, that IS ok. It is an uncomfortable fact that people like to ignore, but it IS ok, because people DO have a right to that money and it is unfair to criticise people for not giving it away. Likewise, people have a right to not want to be overweight all their lives and not have that turned into some weird moral accusation at them.
It's not "I value my looks more than other's lives." It is "I value the right of being the person I want to be, and no-one can take that right away from me."
So the question is useless, because you have no right to make others feel guilty for not sacrificing what they have for the lives of others; modern civilisation simply isn't about that, and would not function if it was. People have a right to what they have, and no social obligation to give it up for others.
In case you have not guessed, my answer is- no, I wouldn't do it, and damn any of you who think that is vain, and I have serious issues with the morality of anyone who thinks that. I might consider it, but to make out I am morally OBLIGED to do it is very wrong, and I would almost certainly reject the deal on that principle alone (that I am damned if I am going to be judged on such an absurd basis)
I think the issue this question raises opens and shuts almost at once- in the Modern World, some suffer whilst others do not- and a certain willfull ignoring of that is needed to survive. If you don't like it, tough, that's how we live; feel free to try and create something better- you never will.