Moi!
An object's weight (not its mass) is a measure of how much the planet Earth pulls on that object. Hold an object in your hand. The weight you feel is how strongly our planet is pulling on it. But that feel of weight is a result of an interaction between the Earth and that object. Sir Isaac Newton established that all bodies in the universe attract each other with a force that increases as mass of the bodies increases. Thus an object's weight depends on two things: how much stuff is in the object itself, and much stuff is in the object pulling on it, in this case, the Earth. It follows that an object's weight is greater in the gravitational field of the Sun, and less in the gravitational field of the moon.
Newton realized that all objects have an intrinsic property that doesn't depend on the planet pulling on the object, a property that stays the same whether or not the object is on the Sun, the Moon, or on the Earth. This intrinsic property of any body, independent of where it is in the universe, is called the body's mass. And a body's mass can be obtained by taking its weight -- which depends on how much a particular "planet" is pulling on it to make it "heavy" -- and dividing its weight by the strength of the particular planet's pull on it.
Now Newton discovered that the Earth pulls on (or accelerates) all objects with the same amount of force. This is the gist of his apocryphal falling apple experience. If you were to drop 1 pound of feathers and a 1-pound lead ball from the same height in a vacuum, they would both hit the ground at the same time. Why "in a vacuum?" Because air resistance would impede the falling feathers more than the falling lead ball -- but they are both being pulled on (or accelerated by) the Earth with one pound of force, which is experienced on the Earth as their weight.
Since the Earth's pull is a constant for all bodies, it can be easily calculated. It is 32 feet/9.8 meters per second per second. The "per second per second" is because acceleration is a change in velocity, so the Earth's pull increases a falling body's velocity 32 feet per second every second. Thus the Earth's constant pull on all objects can be divided out of the weight of any object. And when you divide an object's weight by the pull of the body in whose gravitational field you're measuring its weight (like the Earth's pull), you're left with its "mass" (the units of which are "slugs" in the English system).
Thus a body's mass is independent of the planet in whose gravitational field you're weighing it. So although its weight differs on Mercury, the Sun, the Moon and Jupiter, its mass remains constant on all those bodies. Mass is the amount of stuff a body has in it, not how hard a particular body or planet is pulling on that stuff -- which is its weight.
