In my case, I came out 2 weeks late and was little over 12lbs (~5.5kg) when I did. Apparently birth weight over 9.5 lbs is also correlated with higher rates of ASD. That would be my guess as to why c-sections show a correlation.
1st 8lb. 2nd 8lb, 3rd 10.5lb, 4th and 5th 6.5lb ea (twins). None were c-section.
First 3 were home or birth center, last had to be hospital. My wife had good BMI for the start of each pregnancy.
A friend of mine has 8 childen and none are autistic. All were born at the hospital (this is where you give birth in France), all were notmal weight and so was the mom (and dad)
What led to increased diagnosis of autism was evaluating more kids who had autism.