yeah, there is different levels of fat so it totally depends. i have some chunky friends who know how to dress for their body type and have pretty faces/good personalities so i wouldn't consider that embarrassing.
fugly chicks are a no go, they obviously don't have enough self respect to take care of their bodies, that that in itself is embarrassing. that being said, there are some pretty ugly skinny girls too, and in some cases it might be less embarrassing to go with a fatter, better looking chick then a girl with a face only a mother could love. it totally depends on the situation, the girl as an individual, and the amount of alcohol involved.