As far as weight loss is concerned, adding cardio into your routine will burn calories during the exercise and boost your metabolism to burn even more calories later on. Not only that, but you will start to tone up some of those muscles you do not otherwise use, and building muscle is yet another way to boost your metabolism and increase your resting metabolic heart rate (aka the amount of calories you burn while at rest doing nothing at all). And running is one of the most effective cardio methods for burning calories. So in short, you are smart to start incorporating some running in each week! But while you should start increasing the amount of miles you run slowly, it may be that you will need to do more than just one mile a week. So you are on to something if you are considering increasing to 3 miles.
A general rule of thumb is that, to find out about how many calories you burn per mile while running, multiply your weight in pounds by 0.75. So, you say you weigh 210 lbs so you likely burn around 150 calories each mile. However, that number is still dependent on how fast you are running so to burn even more calories per mile, focus on increasing your speed, which increases your overall exertion effort. When you consider this, 150 calories burned from one mile is significantly lower than 450 calories burned from three miles. That's the difference between a meal and a snack for some people!
While running and increasing your running will definitely help you burn more calories, you might not be seeing any difference in your weight because of your diet. Unfortunately for us folks who love running (and also love food!), running DOES help maintain your weight but it has more to do with what you are eating. A mile burns between 100 and 200 calories, depending on your height, weight, and pace. That isn't even a whole slice of pizza! You can see, then, how easy it can be to undo all your hard work with just a few bad choices at meal times. Focusing on a clean diet, increase your cardio, and you'll more likely start to see the scale go down!