What we think of as weight is the gravitational pull of the earth itself on a person or object.
Therefore, asking the earth’s weight is essentially meaningless, because it has weight only in relation to another object.
However, the mass of the earth, the quantity of matter in it, can be estimated by calculating its gravitational effect on the motion
of an object of known mass.
Basically, if the earth had one mass, it would make things move one way, but if it had another mass, it would make things move another way.
Most scientists give a figure for earth’s mass of around 5.98 times 10 to the 24th power kilograms, or 598 followed by twenty-two zeros.
Before the space age, the estimation process was extremely complicated.
The first reasonable figure for the earth’s mass was obtained by Nevil Maskeyne in 1774.
He estimated the mass of a mountain in Scotland and calculated the approximate effect of its gravitational pull, as opposed to the pull of the earth, on the motion of a swinging pendulum.
These days, better estimates are derived by observing the motion of man-made satellites around the earth.