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This may be more of an explanation than an answer but I hope it helps:
Weight is what causes a balance scale to balance when we put equal mass on each side in the presence of a gravitational field. Since Earth�s gravity is what makes a balance scale work for us here on Earth, when we measure weight we are indirectly measuring the Earth�s mass. But to measure the Earth�s total mass one pan at a time would take some time. Fortunately there is an easier way.
The Earth is constantly accelerating toward the Sun. Otherwise the Earth would travel in a straight line and would not maintain its orbit around the Sun. This acceleration toward the Sun is balanced between falling into the Sun and leaving its orbit by the mutual gravitational attraction between the Earth and Sun (due to their respective masses) and the velocity of the Earth's motion around the Sun which would otherwise send the Earth away from the Sun and out of our Solar System.
Gravity causes acceleration (of a free falling object)proportional to the mass and inversely proportional to the radius squared (the closer to the source of gravity the quicker the acceleration).
When we weigh an object on the Earth the mutual gravitational attraction between the mass of the object and the mass of the Earth is largely determined by the much greater mass of the Earth. The acceleration of one mass towards another is determined by the strength of the mutual attraction between the two objects due to their respective masses and the gravitational constant.
The gravitational constant is universal (the same everywhere) and can be found by measuring the mutual gravitational attraction between two objects of known (measured) mass. Applying the gravitational constant to the corresponding acceleration of Earth�s gravity (at the Earth� surface) gives us the Earth�s �weight�.
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