In the interest of full disclosure, I was not always a fat girl runner. Once upon a time(27 years ago) I was on my high school cross country team. While I was not at my thinnest, I was in good shape.
Since I began running again I have become aware of problems that I didn't have as a thinner runner. I have compiled a few for your reading pleasure.
Clothes- I could probably do a very long post on problems with clothes. Let's start with shorts. In general, plus size runners can't wear cute little shorts. If you are lucky enough to find shorts that claim to be your size they probably aren't really your size or are your size but are cut just a little bit odd. Second, fat girls have thighs that rub together which means that with every step your shorts climb your thighs until you appear to be wearing a diaper. Not attractive. I have read about running skirts. I'd love to try one. If I could find one in my size.
Then there are sports bras. This has always been an issue for me because I have been genetically blessed in. If there were sports bras 27 years ago I certainly didn't know about them.
Now I'm trying to find them in a 42 G. Yeah thats fun.
Shirts are fun too. In fact shirts bother me so much I made my own. It says " Yes, I'm fat AND I'm running. Encourage me, run with me or get out of the way!"