Mass is the quantity of matter an object has and it is measured in kilograms and weight is the *ahem* gravitational “force” that is attracting the objects towards the Earth and it is measured in newtons. Professor Mike Merrifield from the University of Nottingham explains why mass and weight are almost the same.
When we talk about mass, we know that we look at mass from two different perspectives: inertial mass, F=m*a, where we look at how hard is to push an object and gravitational mass, F = G m1 m /r^2. When we put the two formulas together, a situation in which we let an object in free fall then we get this:
F = m*a = G*M1*m/r^2.
M1 is Earth mass, m is the object’s mass. As you see, putting those two together will tell a thing: mass does not count in that situation. Letting two different objects with different masses in free fall it will make them fall at the same rate and that is g=9.81 m/s^2. Neat, eh?
Here we talk about the Equivalence Principle, where we associate the mass that is associated with how hard you have to push an object (inertial mass) with how gravity pulls on things (gravitational mass).