Gravity is a force that pulls on things. Just like if you push something across the table, your push is a force. There are many different types of forces, but forces are not physical objects, they are more like actions. Since forces are not objects, they do not have mass. How much something weighs is determined by multiplying the mass of the object by the force of gravity acting on the object.
Forces have no mass, so they never weigh anything.
Things that don't have mass, that arent' made up of atoms, don't weigh anything. Also, objects in space don't weigh anything because there isn't any gravity. So, even if an object is very large, if there isn't any gravity, it doesn't weigh anything. I hope this helps you understand a little better. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.