I read this yesterday, and was quite Hm. about it all.
For a start - there is a massive recession are. There are tons of people interviewing and applying for jobs with little or no success, and it's because there aren't many jobs going around. She might not be getting jobs that she is over-qualified for because ... she's overqualified! and employers think she'll be unhappy, and leave as soon as there's a better opportunity and finally, because she probably commands a higher salary than someone less qualified. It could also be down to attitude - she does sound resentful and defeated, and that will come across in interviews.
Yes, there is prejudice against people who are overweight, but not every single employer is fattist, much like not every woman is insanely jealous of Samantha Brick's breathless "beauty", but that wouldn't work in a DM article "some people are prejudiced and there's a recession on so someone is struggling to get a job" just isn't as catchy as "Get a job at my size? Fat chance"