Final answer:
The gravitational force between two objects will be most significantly increased by either increasing their masses or decreasing the distance between them, with a greater effect from increasing mass.
Step-by-step explanation:
According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
To increase the gravitational force between two massive objects most significantly, one could either increase the mass of one or both objects or decrease the distance between them. However, since the force increases with the product of the masses and decreases with the square of the distance, doubling the mass of one object would have a more substantial impact than halving the distance between them.