A satellite stays in orbit because gravity provides the centripetal force it needs. This fixes the orbital velocity for each orbit radius. The speed does not depend on the mass of the satellite, and it is smaller in a larger orbit.
Your real weight is the pull of gravity, mg. Your apparent weight is the force a scale or floor exerts on you. In a lift accelerating upwards it is more than mg, and accelerating downwards it is less. In free fall, or in orbit, you and the floor fall together, so the contact force is zero. This is weightlessness, even though gravity still acts.
A geostationary satellite takes 24 hours to orbit above the equator, so it stays over one place on the Earth.