Lunch/coffee dates with friends definitely constitute as "busy" so... when you see someone out for lunch and you feel like they bailed on you? They likely had those plans already made - just like you now have for later this week!

Depression definitely gets in the way. When you're depressed, do you slack off on hygiene? That's more of a turn-off for people than someone's body size when it comes to making friends.

Are you trying to be friends with people who are a lot younger than you? I'm not clear on that as you are in a university area. You're not working on the same degree as younger students from the sounds of it. Different age gaps and life situations do tend to play a role in developing friendships.

Some of the most confident and well respected people I know are heavy. They look amazing and some of those people have the best put-together looks I have seen! They pay attention to their appearance, but it isn't the size that influences how people percieve them, but how they take care of themselves. They are by leaps and bounds more attractive than I am - because when I'm depressed/exhausted/anxious I totally throw out "put together a nice outfit" and end up with no make-up, hair a disaster (my hair hates to cooperate on the best of days) and fairly random clothes tossed on. But when I'm doing fine, I'm more on par (I always do minimal make up really, I'm never 100% "put together"... joys of being female...).