Can we find the weight of the earth (not mass)?

Yes, we can. The earth is in free fall, but it is not weightless. The weight of the earth is the total gravitational force on the earth. The primary source of gravity is the sun. The moon also has some effect, though it’s obviously much smaller, because if it were much larger, it would cause a noticeable wobble in the Earth’s motion. read more

Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. 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