Type 2 Diabetes has a "weight" connection because glycologen (sugar) is stored in fat cells. Therefore if you already have a genetic propensity to have a low functioning pancreas combined with becoming overweight, then your risk will go up.
However, people that don't process their carbohydrates properly (into energy rapidly, usually) gain weight easily and are in an insulin resistant or pre-diabetic state. So, this becomes a bit chicken and egg.
My family has lots of overweight people and lots of Type 2 diabetics. They do not always go hand in hand. My endocrinologist office waiting room is a mix of people overweight and not with both types of diabetes. I have gone to nutrition and cooking classes for diabetics and everyone there was certainly not overweight and I mean the Type 2's.
I only want to point this out as there is starting to be some hurtful things said in the media and online that almost seeks to pit Type 1 and Type 2's against each other. I saw one woman point out on a forum that she had "type 1, you know the kind that wasn't my fault." No one needs that kind of stigma attached to a disease that can shorten their life, cause their kidneys to fail, raise their risk of heart attack or cause them to have a limb amputated.
Just an FYI.