As myths go, this is one our all-time favourites, since gravity is one of the four universal forces, along with electromagnetism, and the weak and strong nuclear forces. In fact, gravity holds the Universe together, and although there are other forces at work, like dark matter and dark energy, we will stick with gravity.
Think of gravity this way; your weight, or more precisely your mass, is the sum total of the gravitational effect the earth exerts on every single atom in your body. This is why you feel your own weight when you stand, and if you step on a scale, the figure you see is the effect of gravity on your body, but expressed as a numerical value.
The reason this is so is because you are not in freefall around the earth, as astronauts in a spacecraft are. In their case, they are in freefall around the earth, but there is no difference in the rate at which they fall, and the rate at which the spacecraft is falling. In other words, they are falling around the earth at exactly the same rate, which means that inertia does not enter into the equation. Inertia is the resistance a body shows to movement, so as long as the astronauts and the spacecraft fall at the same rate, it will seem as if gravity has no affect on them, and they will remain stationary with respect to everything else around them.
However, if an astronaut launches himself from one point of the spacecraft to another, he will possess momentum, and if he does not control the rate at which he accelerating in a different direction, and at a rate that is different from that at which the spacecraft is falling, he can knock himself out against, say, an opposite wall since he still has mass.
The same thing happens on a larger scale in outer space. For instance, the earth is in freefall around the sun, but since it is moving at a high enough rate to avoid being captured by the sun, it will continue to orbit the sun, but the sun’s gravity is nevertheless strong enough to keep the earth from sinning away into space. On an even bigger scale, the entire solar system is orbiting the centre of mass of the Milky Way, but at a rate that is too fast for the mass concentration at the galaxy’s core to pull the solar system straight towards it.
And so on, and so on. Everything in the Universe that has mass exerts a gravitational influence on everything around it, but since the strength of gravity decreases with distance, it is not correct to say that everything in the Universe affects everything else. Some objects are just too far apart for their gravitational fields to interact, but with really massive objects like galaxies, it is possible to see the effects of gravitational interactions over thousands, and even millions of light years as the interaction tears the galaxies to shreds.