I have been using a C-Pap machine for 14 years now...and yes, I am overweight. However, one of my friends who also has SA and uses a C-Pap machine is about 100 pounds dripping wet, at 6' tall, so it doesn't just affect fat people.
I snored terribly for years, even before I gained weight...and this was before I was overweight. My wife told me constantly that I gasped and choked in my sleep, so mine may not be weight related. It finally got to the point that I was falling asleep in meetings, while driving, etc., so I went to the doctor. At the sleep study, they told me I had horrible SA, and they put me on a machine that night...and I had the sweetest sleep I can ever remember!
The only time I've had a problem traveling was when I checked my machine on a flight (it was inside my suitcase.) When I got to the hotel that night, and got out my machine, I discovered that my plastic mask had broken in several places. As a result it leaked air badly. I went to a drug store and got some tape to try to repair it, but that didn't work...so I had the BRILLIANT idea to try super glue. It worked...at least the mask held together and all the fractures were sealed...but the fumes nearly killed me!
I was flying home the next evening, so I just toughed it out. Otherwise, I've never run into any problems traveling. I sleep very well with my machine, and it doesn't bother me at all.