What is the relationship between mass and gravitational force between any two objects?

If two objects' mass increases, gravitational force pulls them down to the center more strongly because the greater the mass, the stronger the attraction is from the gravitational force from any two objects. An increase in then Earth's mass and increase in a man's mass would make gravitational force pull more strongly on the person because the Earth's gravitational force multiplied from the mass change and the man's greater mass pulls them down more quickly.