How many calories should an overweight thirteen-year-old boy have a day?

That depends on a few factors. Current weight and activity level are key. Also, are you asking how many calories he should have to maintain his current weight or to lose weight? If he wants to lose weight a ballpark calorie count can be found by looking at the desired weight's daily calorie needs in any calorie counter book. For instance if he wants to weigh 150, he should look at a calorie chart for someone who weighs 150 lbs. If you google "calorie counts" you will get many helpful hits.