I'm fat. I've cooked the vast majority of my food since I was 19 or so (I'm 28 now) and I've lost some weight, gained some weight, been more and less active, but always been fat. That said, I do also have a kind of broken endocrine system (PCOS, HGH deficiency), so I may not be a great test case. I am also healthy by other markers—blood pressure, cholesterol numbers, triglycerides, hip/waist ratio, etc.
I do think that home cooking (from quality, whole ingredients) goes a long, long way towards health, but I don't think it's a guarantor of thinness. Then again, I also don't think being fat is in and of itself a death blow or that thinness is an indicator of health, but that conversation is probably not worth having here.