Plus Size Delivery

Emily
Sooooo, I've seen it bandied about that there's an increased likelihood of plus size women needing c-sections, and I'm trying to get at the specifics of that claim...
For those of you who already have kids, did you deliver vaginally or surgically? And if you had to have a c-section, was it because of medical issues like your blood pressure, baby's heart rate, etc? Or was it because of your physiology? 
I just find it hard to believe that my vagina is "too fat" to have a baby (I mean, nobody has said this to me explicitly, but on Glow and in the real world it has been implied).