You don't sound like a weirdo at all. That's because American (and Korea, Japan, Brazil, etc.) society judges a woman's worth by her looks. It is not this way with close friend's and family but if you go to a party, wedding or job interview, many are sure to make a judgement based on how you look. It puts terrible pressure on women and lately I think that even men are starting to feel pressure in this regard.
I know it's easier said than done but it is important to get to a place where you are exercising and losing weight for your health and well being, not to conform to unrealistic and unhealthy standards.
None of us have a perfect soul! But good people try to overcome their weaknesses in regards to patience and kindness. You really sound like a very kind and sensitive person. The fact that you don't want to burden your family and don't want to disappoint your friend shows that you care about others feelings/needs. That is a very good thing about you that does not need to be fixed!
I hope you feel a little better today than you did two days ago. Please keep posting.