When making measurements of the earth's gravity, we usually don't measure the gravitational force, F. Rather, we measure the gravitational acceleration, g. The gravitational acceleration is the time rate of change of a body's speed under the influence of the gravitational force. That is, if you drop a rock off a cliff, it not only falls, but its speed increases as it falls.
In addition to defining the law of mutual attraction between masses, Newton also defined the relationship between a force and an acceleration. Newton's second law states that force is proportional to acceleration. The constant of proportionality is the mass of the object.
Combining Newton's second law with his law of mutual attraction, the gravitational acceleration on the mass m2 can be shown to be equal to the mass of attracting object, m1, over the squared distance between the center of the two masses, r.