These statistical studies may or may not imply causation.
Let’s postulate that obesity is a marker for lower-class women. There might be many other factors in lower-class households that would also leave to autism. Poor nutrition, excess TV watching, lack of parental attention, etc.
Perhaps, but my son is severely dyslexic and has suffered from language based developmental delays that are so extreme that he didn't even talk until he was about five years old. His mother (my ex), was not by any measure obese, but she did have gestational diabetes that required hospitalization. She is also very bright with near perfect SATs, and BS, MS, and MBA degrees.
I think obesity is more likely to be a precursor or indicator for diabetes more than social class.
My SIL is an MD, not obese (actually tall and slender) but she had gestational diabetes with her first child and he is autistic.