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.
Inertia
This was clear at the beginning of the 20th century, before the advent of the theory of relativity. Mass, "m", denoted something like an amount of substance or quantity of matter. At the same time, mass was the quantitative measure of inertia of a body.