My mother had type 2 diabetes, and she was not overweight, yet there are so many overweight people who do not have diabetes. Why is this? 
— Carmen, New York

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Yes, your observation is accurate and reflects the complexity of diabetes and the problem with our current classification system. The simple classification system of diabetes as type 1 and 2 does not reflect the fact that diabetes is a collection of many different conditions that cause high levels of sugar in the blood stream. There are close to 30 defects and conditions associated with either insulin resistance or insulin deficiency, which are the two basic mechanisms for diabetes. A few of these defects are genetic or hormonal; others result from autoimmune disorders, viral infections, or injuries to the pancreas. While type 1 diabetes is caused by the antibody-mediated destruction (autoimmune disorders) of the pancreatic cells that produce insulin and usually occurs among infants and children, type 2 diabetes is commonly associated with insulin resistance and is diagnosed among adults. Having said this, there are a growing number of overweight and obese children who are developing type 2 diabetes and a few adults who have type 1 diabetes.
Let me define insulin resistance, which is linked to type 2 diabetes, and explain why weight is associated with it. Insulin resistance is a condition whereby the pancreas releases an adequate amount of insulin but the body's organs, primarily the skeletal muscle, the liver and fat cells, do not respond to the insulin or utilize glucose normally. This causes sugar to accumulate in the blood stream, leading to the typically high levels we see in diabetics. Any number of the steps in the glucose metabolism (e.g. how the body burns sugar for energy) pathway may be the underlying cause of insulin resistance. Some of these are specific genetic defects but the more common cause is excessive weight. Excess fat in the body releases at least three different types of metabolic products, which cause insulin resistance. To make matters even more confusing, not everyone who has excess fat develops insulin resistance enough to cause diabetes.
Most overweight and mildly obese folks who go on to develop diabetes also have a family history of the disease or carry other risks such as advancing age, low birth weight or are subject to other environmental and yet undiscovered triggers. These factors usually lead to pancreatic dysfunction so that the pancreatic cells are not producing an adequate amount of insulin, enough to compensate for the insulin resistance. Family history of diabetes might skip a generation and the environmental conditions might not be detected.
In a nutshell, among many overweight individuals, diabetes is caused by a combination of factors, excess weight causing insulin resistance and other factors limiting the ability of the pancreas to compensate for the insulin resistance. Hence, not all overweight individuals develop diabetes. And because there are reasons other than excess weight to develop insulin resistance such as genetic defects as mentioned above, not all individuals who have diabetes are overweight.
How is this for a long-winded and convoluted answer? It mirrors the current state of diabetes. More research will help us classify diabetes better in the future.