I think what AFrozenSoul is saying is that it is *because* you care about them that you feel they should lose weight. (I just noticed bookbinder has made this point ahead of me.) Other examples would be to ask your partner to stop smoking, or stop taking drugs, or stop drinking too much, etc. If you can see that these habits are having an unhealthy impact on them then you would want them to stop. Of course sometimes the situation isn't so clear cut - you wish the person you were dating would dress better, and you're sure it would benefit them to do so, but is it really a matter of self-destructive behaviour or just a matter of taste?
I've been in relationships where I've been pressured to make changes to myself. I think this is actually pretty normal, and initially I'm happy to try and accommodate the other person as much as possible without making too many demands of my own. The trouble is that there are some things you can't change about yourself without ceasing to be the person that you are. I believe it's very important that both partners try to figure out where these boundaries are drawn and try not cross them - otherwise what you're really saying is that you wish you were going out with someone else.