I too have noticed a connection between obese people and no acne --- but I have also noticed a connection between people who eat @#$% and still have clear complexions...something which is often brought up by angry fed-up acne sufferers on this site. Here is my take on this.
Acne sufferers usually very quickly consciously or unconsciously notice a connection between foods and breakouts. I remember as a teen noting this and avoiding chocolate and milk because they immediately caused flare-ups. I also began noting that if I ate healthier my skin seemed to do better...not clear just better. Consequently over the years I maintained a healthy weight because I very consciously was trying to do everything I could to avoid flare-ups. Yes, because I have struggled with severe acne I became obsessed with diet as a means to control flare-ups...but it helped so I continued. Flash forward decades and if you compared me to others my age you would say I looked like someone in their 20's physically, whereas most of my peers are overweight and suffering from diabetes and other internal inflammatory diseases. They may not have acne but they have far worse diseases!
Why don't they have acne? Well, they were never predisposed to it genetically. They could keep on eating whatever they liked with seemingly no consequences...so they did. When we'd go out to eat they'd go for the heavy cream based sauces and I would be eating a huge salad. They drank lots...because nothing caused a flare-up. If it had you'd better believe they would have stopped because acne is so embarrasing! But their bodies did not flame up this way...they were not sensitive to androgens genetically (like me) so they kept on eating whatever they wanted and too much. But all this inflammatory eating did catch up with them...believe me! They have far worse problems and take far worse drugs with awful side effects.
Yes, I take 2 meds for my acne/rosacea (low dose spiro and extremely low dose anti-inflamatory dose doxy) but they have no side effects other than I have to pee an hour after taking spiro because it is a mild diuretic.
Here's something to console yourself with if you suffer from chronic acne. Your early efforts to eat right in order to manage your skin's inflammatory response (acne) will pay you back tenfold later when you are healthy, strong, fit and able to do marathons like me...and I am 62!
Those people who ate @#$% and had clear skin will keep on eating @#$% until their bodies break down in some other more devastating way.