*CoMmOn MiScOnCePtIoNs*
"Anorexics are always underweight, Bulimics are always normal weight, and Complusive Overeaters and Binge Eaters are always overweight."

This is NOT so.  An anorexic can weigh 200 pounds (say, the person used to weigh 260 lbs), a bulimic can weigh 300 pounds or 80 pounds, and a complusive/bing eater can weigh 110 pounds.  THE WEIGHT IS NOT THE ISSUE!  THE ISSUE IS:  THE MINDSET!!!  A 200 lb person can be just as obsessed with exercise and counting calories as someone who is of normal weight or underweight!  There are plenty of binge eaters who are also athletes and thus work off the calories (but are not exercising as means of purging), and maintain a normal weight, and there are bulimics who also restrict (sometimes called bulimiarexia), and bulimics who take in 10,000 calories per binge - imagine if you only "get rid" of 5000 of the calories- you still digest the other 5000, thus bulimia can frequently lead to weight gain.
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"Anorexics just need to EAT MORE, and bulimics and binge eaters just need to EAT LESS!  What's the big deal??"

An eating disorder is NOT about the food.  The food is just the "drug" of choice.  Eating disorders are about what drive a person to starvation or bingeing and/or purging.  The behavior with the food is just a symptom of  the REAL problem, and the person cannot simply just adjust their food intake to "NORMAL" (which, really, what IS normal?) until they have dealt with the feelings and issues that have led them to abuse food in this way.