The term 'metabolic rate' refers to the energy (calories) you expend over a day just keeping your body functioning - your heart beating and your lungs breathing, for example. This is often called the basal or resting metabolic rate.
Scientists have measured the exact amount of calories overweight and healthy weight people burn while sitting or lying quietly. This was done by measuring the amount of oxygen breathed in and the amount of carbon dioxide breathed out.
Results from these studies have consistently shown that overweight people use more energy to keep their bodies working. This is because they have larger bodies with bigger muscles and internal organs.
However, after taking into account differences in body size, lean and obese people have been shown to have similar metabolic rates.
Basal metabolic rate can be influenced by body composition. Muscle requires more energy to function than fat. As we get older, we tend to gain fat and lose muscle. This explains why basal metabolic rate tends to decrease with age.
Similarly, two people of the same age and weight may have different metabolic rates if one is fitter (and has more muscle) than the other.