I'm going to assume that you know that all that extra weight is fat, not muscle, because obviously muscle doesn't count in being overweight (not that the BMI will tell you that).
Your case does sound very unusual--most people with D that bad are on here asking how to gain weight; you may have a metabolic problem or outright disorder. Honestly, there really are some people out there who are fat no matter what because their bodies don't burn calories even approaching correctly. You might try a doctor that knows something about those kinds of disorders (usually genetic) who can test you for them. There may or may not be any medicine to help it.
Even if you don't have a true metabolic disorder, consuming too few calories can actually cause you to stop losing weight, as your metabolism slows down to compensate. That's why throughout history there have been people on starvation-ration diets who lived for years like that (we're talking around 500 calories a day, and very unbalanced in terms of nutrition). The only way I can think of raising your metabolism without fiddling with your diet (you have to eat what you can tolerate!), is for you to lift weights/do strength training. Muscles work (fat stagnates), therefore they require calories in order to function. So working your muscles burns calories and building more muscle burns more calories. Also, if you can get in several small sessions throughout the day, you will be revving up your muscles and they will be active (even for a while after you stop exercising) and burning more calories.
Just know, though, that muscle weighs more than fat, so you may not notice a dip in the scale, even though you have made improvements to both your body and metabolism. However, muscle takes up less space than fat, so you can usually tell a difference in how your clothes fit.