What does the Earth have, mass or weight?

Yes, it has weight. Every piece of the earth is being pulled by gravity toward the center of mass (adjusted for the gravitational fields of OTHER bodies, like the moon and sun, primarily) The weight of the earth would be calculated by determining the weight of each layer, like an onion. read more

1 It is "more proper" to ask about mass rather than weight because weight is a force that requires a gravitational field to determine. You can take a bowling ball and weigh it on the Earth and on the moon. The weight on the moon will be one-sixth that on the Earth, but the amount of mass is the same in both places. read more

Similarly, a balloon has mass but may appear to have no weight or even negative weight, due to buoyancy in air. However the weight of the balloon and the gas inside it has merely been transferred to a large area of the Earth's surface, making the weight difficult to measure. read more