If we were going to exaggerate examples you might just as well have said 400lbs @ 12mph. When you're seriously overweight the best approach is diet first, exercise later. One of the most prominent reasons is for the sake of your knees. Running with extra weight puts a lot of pressure on the joints and can cause permanent damage, especially at 250-320lbs. Eating a better, lower calorie diet will help you drop the excess weight until you're at a healthier point. From then on, you can start doing a routine that suits your goals (ie. weights 3-5 times a week with cardio on off days).
You need all three things (diet, resistance, cardio) to be truly healthy AND fit. You can be skinny from just running, but for most people that's not their goal (in fact, it would take longer).
Eat less, eat clean, lift more. You'd see the most benefit at your weight. You've built some strong muscles from carrying around the extra weight, it would be a shame to waste it all by running until you're skinny.