Acceleration due to gravity is acceleration due to free fall. All heavenly bodies are free falling , that is why it is moving in a circular path . The acceleration due to gravity is smaller further away from the centre of mass therefore the angular velocity is smaller , hence period is longer , velocity is smaller.
Standing on the Earth ,one is not falling and therefore one is not orbiting. Standing on the ground one can feel one's weight and therefore a person orbiting is falling and cannot feel weight and therefore is said to be experiencing weightlessness. Expriencing weightlessness does not mean the person does not have weight. The weight of the person is present and responsible for the falling ( orbiting)
