The authors note their finding shows how the body adapts after weight loss blocks successful weight maintenance. Part of this effect is the reduction in energy required to move a leaner body.
For example, if you walk a mile when you weight 200 pounds it takes a certain amount of energy. If you drop your weight to 150 pounds you burn fewer calories when walking a mile. Part of the adaptation is a dialing back of the bodies energy expenditure with weigh loss. The implications of their findings are that after successful weight loss, it may be necessary to increase exercise time or intensity.