Body size affects energy expended for physical activity is TRUE.
Expenditure of energy is found by the body size and body composition of the being while doing any physical activity. Higher weight has a higher energy requirement. It needs higher maintenance and higher resting requirement also.
Smaller and leaner objects move with more active energy as the physical activity required in doing so is less. Since they have less body weight and require less maintenance their energy requirement is less. Hence energy expended is also less in such cases.
In any physical activity, there cannot be a comparison between smaller and heavier beings' amount of expending energy since it depends on the speed, effort, work out efficiency and time taken by them. But, body size certainly affects energy expended during any physical activity.