It is called so because it is applicable on all bodies having mass, and the bodies will be governed by the same law, that is newton's law of gravitation. Thus, as it is applicable universally, it is called as universal law.
Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases.
