Type 1 diabetes is not associated with being overweight and weight loss does not help. Indeed, rapid weight loss is often an early indication of the condition. Treatment with insulin (the only method available) typically results in weight gain, as the body recovers due to the newly available injected insulin. Often these patients start at normal weight range (i.e. BMI < 25) and are often substantially below typical weights prior to development of diabetes.
Type 2 diabetes has strong genetic factors and substantial evidence shows these, combined with weight and some other factors of diet, lead to an expression as diabetes. In these cases, some people have had significant improvements in their conditions due to calorie restriction (leading to weight loss but often it also means they've switched to a healthier diet in the process and that also helps). The mechanisms here are believed to be due to improved sensitivity to insulin which is still being naturally produced.
Various ratios of diabetes are quoted, but generally 1 in 20 of the white european population has diabetes and 1 in 20 of those has type 1 (and the other 19 type 2). Figures for Indian/Pakistani origin people are dramatically different if they move to Europe or North America and research suggests this is due to very different foods consumed [the 'western' versions being significantly less healthy than those from origin countries]. Much higher numbers of type 2 diabetes are found in these populations (reinforcing the factors as both genetics and types of food are involved). Other population groups differ too.
Treatments for diabetes typically create weight control issues as increased insulin or sensitivity to insulin promotes body fat storage.
It's untrue (and frankly verging on offensive) to simply blame diabetics for their condition because they are obese or overweight. Addressing and treating the condition is significantly more complex and weight control may be one of the few elements the patient has any input to, while many other factors are entirely outwith their control and they bear no culpability for.