Genetics plays a role in Type I && II (but not in gestational or (sometimes) ones involving injury.
Overweight can be a side effect of Diabetes...(and not eating right can affect you getting Type II diabetes) I know diabetics (who don't handle their sugars properly) who have gotten heavily overweight. I know others who have watched their weight and reversed diabetes.
But my Grandfather was rail-thin and had to take insulin the entire time I knew him.