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The main reason why fat people have less acne is that the toxins that purge out of the skin in acne are stored on the fat.
And skinny people don't have enough fat to store the toxins so they purge them out of their skin.
Sudden fat loss can cause sudden acne as the toxins are purged out of the fat via acne.
This means fat is protecting your all organs (skin is organ), by keeping the toxins in the fat and not letting them go to critical organs and tissue.
Body dumping the toxins through skin as acne is more healthy than dumping them deeper inside towards organs.
Skinny people not having acne is sign of malnutrition, specifically sign of liver issue (detox organ), as their body can't produce acne despite toxins coming from industrialized foods and environment and those toxins are needed to be detoxed, most very skinny people in modern world should have some acne if not on rawprimal
Here are objective statistics, (don't trust WHO on health advice):
According to World Health Organization BMI definitions of underweight, normal weight, overweight, obese and severely obese, the researchers found overweight youth were 20% less likely to have acne than normal weight adolescents.
Obese adolescents were 35% less likely and severely obese youth 50% less likely to have acne than normal weight teens.
With each one-unit BMI increase, the odds of acne decreased by 3.2%, according to the study.