Would you weigh anything on the moon?

Yes. The Moon has gravity, just much less than Earth. Measured on a scale, you would weigh about 1/6 as much on the Moon as you do on Earth.

The reason that astronauts weigh almost nothing in orbit, or in outer space on the way to the Moon, has nothing to do with the vacuum of space (there is a practical vacuum on the Moon). In Earth orbit, they are in freefall around the planet, so have no weight. And in outer space, gravity decreases tremendously with distance. At about 2500 km (1500 miles) from Earth, the pull of Earth's gravity is only half as strong as it is on the surface.