I always thought it was because when a heavy person does physical activity they are putting a bigger strain on the heart thus burning more cals as it pumps faster, the thinner they get, the heartbeats work at a slower healthier rate and burn less calories.
The number of calories burned is dependent on:
The amount of time spent on physical activity. For example, walking for 45 minutes will burn more calories than walking for 20 minutes.
Your body weight. For example, a 150-kilo person will expend more energy walking for 30 minutes than a 85-kilo person.
Pace: For example, walking 3 miles per hour will burn more calories than walking 1.5 miles per hour.
BASAL METABOLIC RATE
Your basal metabolic rate (BMR) is the number of calories used by your body when it is at rest. BMR accounts for most of your calorie use. Your basal metabolic rate is based on body functions such as breathing, digestion, heartbeat, and brain function. Your age, censored, body weight, and level of physical activity impact the basal metabolic rate. Basal metabolic rate increases with the amount of muscle tissue you have, and it reduces with age.
Along with burning more calories, physical activity increases the BMR, and the BMR can remain increased after 30 minutes of moderate physical activity. For many people the basal metabolic rate can be increased 10% for approximately 48 hours after the activity. This means, for example, even after the physical activity, when a person is sedentary and watching television, the body is using more calories than usual.