An artificial satellite revolving around the earth in a circular orbit is in a balanced condition. The centripetal force of the satellite is equal to the gravitational force between the earth and the satellite. So, the only force of gravity experienced by the person is that which is due to the gravitational force exerted by the satellite. But the satellite is small, so this force is negligibly small and the person does not experience any gravity and hence feels weightlessness.
But when the person is on the moon, he/she is acted upon by the strong gravitational force of the moon because of its high mass. So, the person will have some weight on the moon.