The Earth is in free fall around the sun and it actually weighs nothing. The same goes for astronauts in orbit; because they are technically falling around the Earth — and if they stood on a scale, it, too, would be falling — the scale would read zero.
It would be more ideal to ask, "What is the mass of planet Earth?". Mass is a property that is independent of where an objct is in the universe or what it is doing. The quick answer to that is approximately 6,000,000, 000,000,000,000,000,000 (6 x 1024) kilograms.
The measurement of the planet's mass is derived from the gravitational attraction that the Earth has for objects near it. It turns out that any two masses have a gravitational attraction for one another. If you put two bowling balls near each other, they will attract one another gravitationally. The attraction is extremely slight, but if your instruments are sensitive enough you can measure the gravitational attraction that two bowling balls have on one another. From that measurement, you could determine the mass of the two objects. The same is true for two golf balls, but the attraction is even slighter because the amount of gravitational force depends on mass of the objects.