How does the gravitational force between objects change if one object increases in mass but the other does not increase?

The gravitational force depends on the PRODUCT of the two masses. It doesn't care how big or small each individual mass is.

Anything that increases the product of the masses increases the gravitational forces between them.

If one mass increases, then their product increases, and the gravitational forces between them increase.

Here's an example in the real world:

You eat steaks, shakes, and potatoes every day for a week. Your mass increases. The Earth's mass doesn't change. But even so, the gravitational force between the Earth and you increases. (It's called your "weight".)

it doesn't. it was imagined up in the middle ages.