Question

When the mass of an object increases, the force of gravity

Answer 1

Increases

the amount of directly tied to the mass of the object... if the object has less mass, so does the amount of gravity...

Answer 2

The forces of gravity between two objects depend on the masses
of both objects.  So if one mass increases, then the objects will be
drawn together by stronger gravitational force.

Example:
When a person eats a lot of steak and fat and carbohydrates, his
mass increases, and the bathroom scale shows that the gravitational
forces drawing him and the Earth together have increased.  We say
that he has "gained weight".