Question

What effect does Earth’s gravitational force have on objects of different masses?

Answer 1

This is similar to a question I was just in. It might have more insight.
http://openstudy.com/study#/updates/51e30b1ee4b0d9a104dc0ea5

Basically, all masses will have the same gravity-caused acceleration if they're at the same distance from the Earth's center of gravity. The masses might have different accelerations due to different reactions to other forces.

That is disregarding the size of the object, which could complicate things if the object was closer to Earth-size.

Answer 2

the gravitational force will be mass of the object times a constant { known as acceleration due to gravity}. The for we can call as gravity or the weight at that place

Answer 3

Gravity has no effect on the mass of an object. However, an object's weight is the measurement of gravitational force on the object.

The gravitational force on the moon for example is ~ 1/6 of that on Earth.
A 300 kg object would weigh 3000N (Newtons) on the Earth but only weigh 500 N on the Moon but its mass would still be 300 kg on the Moon and on the Earth.