People who are obese have higher rates of medical problems. Once a person reaches the level of "morbid obesity," which by definition is a BMI greater than 40, then the weight causes progressive and extensive damage to the body.
The medical complications of obesity may occur in moderately obese people, but the frequency of these associated problems, such as heart disease, high blood pressure, diabetes, premature death, etc., increases dramatically as weight increases. For example, very obese men between the ages of 25-35 are at 12 times greater risk of dying prematurely compared to their normal weight counterparts.
Severe obesity causes damage to nearly every organ system. We’ve listed some serious medical conditions for each organ system that are commonly associated with obesity. One key thing to remember is that much of this damage can be stopped or even reversed by significant weight loss. Take a look at the page on the health benefits of surgery to get some examples and data.

Cardiovascular system
→ high blood pressure, heart failure, heart attack, stroke
Pulmonary system
→ obstructive sleep apnea, asthma, bronchitis, fluid buildup on the lungs, breathing failure
Gastrointestinal and abdominal
→ gallstones, Gastro Esophageal Reflux Disease (GERD, recurrent heartburn), recurrent ventral hernias, stress urinary incontinence
Endocrine system
→ diabetes, hirsutism (excess hair for women), hyperlipidemia, hypercholesterolemia
Genitourinary, Reproductive
→ high risk pregnancy, increase rate of fetal obesity, stress urinary incontinence, irregular menses and infertility
Bones and joints
→ degeneration of knees and hips, disc herniation, chronic low back pain
Skin
→ multiple disorders, most related to diabetes and difficulty with hygiene
Increased risk of cancer
→ breast, endometrium, colon, prostate, and others