Your weight is the manifestation of the Earth's gravitational attraction of you to it. Your weight is "how much the Earth loves you". Every object on Earth has weight.When a satellite is orbiting the Earth, it is falling towards the Earth because of its weight. Fortunately, it is also moving forward at some speed. When the forward speed and the falling tendency are balanced, the satellite never loses altitude. It remains the same height off the surface of the Earth. It is orbiting the Earth.The Moon is a satellite of the Earth, the only universally acknowledged natural satellite of Earth. Its orbit is stable, but the orbit changes over a long time: the Moon migrates outward, stealing some of the Earth's rotational energy. Subsequently, the Earth slows down. About 250 million years ago, the average solar day was about 23 hours; now its 24 hours.It's not correct to say that astronauts in the Space Station experience weightlessness. They, and the entire Space Station, are freely falling towards Earth, as all satellites do, precisely because they have weight.What is correct to say is that the astronauts are freely falling toward Earth under the influence of gravity, and this experience is equivalent to them being in a region of space where there is no gravity. This is one way to express the Principle of Equivalence, first stated by Albert Einstein almost a century ago.Note that a satellite's orbit is determined only by its orbital speed and the object it is orbiting (here Earth), if the orbit is circular in shape. The orbit that a satellite has around Earth is not a function of the satellite's mass (assuming the orbit is essentially circular, which is generally fair to do).