Why does space weigh nothing?

Answer

Something weighs when it is drawn to something else by its weight. We (and the air too) weigh because the earth pulls on us. It is because the earth with all its mass is below us that we are drawn downwards. Someone on the other side of the Earth is also attracted downwards, but his ‘down’ is ‘up’ for us.

When you are pulled equally hard in all directions, you will not fall, but you will float.

Planets are attracted to the sun. If they started from a standing position, they would fall on the sun, just as we fall from a tree to the ground. But they don’t start from standstill, they have a speed away from the sun. That way, they keep spinning around the sun. You can call it ‘floating’, but that’s a bit misleading. The planets feel no inclination at all to fall above or below their orbit around the sun, for there is nothing close by to attract them.