Weight
In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a "force" that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.
Earth mass
The Henry Cavendish (1798) was the first to attempt to measure the gravitational attraction between two bodies directly in the laboratory.
Earth's mass could be then found by combining two equations; Newton's second law, and Newton's law of universal gravitation.