What force would cause that to be?
Every force has an equal and opposite force. No "up" or "down" without gravity. Attempts to make artificial gravity (say by rotating a spacecraft) would produce anomalous effects not seen in gravity.
The Cavendish experiment shows that gravity exists, even in very small objects:
T
he Cavendish experiment, performed in 1797–1798 by British scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory[1] and the first to yield accurate values for the gravitational constant.[2][3] Because of the unit conventions then in use, the gravitational constant does not appear explicitly in Cavendish's work. Instead, the result was originally expressed as the specific gravity of the Earth,[4] or equivalently the mass of the Earth. His experiment gave the first accurate values for these geophysical constants. The experiment was devised sometime before 1783[5] by geologist John Michell,[6] who constructed a torsion balance apparatus for it. However, Michell died in 1793 without completing the work. After his death the apparatus passed to Francis John Hyde Wollaston and then to Henry Cavendish, who rebuilt the apparatus but kept close to Michell's original plan. Cavendish then carried out a series of measurements with the equipment and reported his results in the Philosophical Transactions of the Royal Society in 1798.[7]
https://en.wikipedia.org/wiki/Cavendish_experiment
Obviously, nothing of the kind would be measured on a flat, unmoving Earth.
Actually, they will. Cavendish measured how much, and essentially determined how much force is exerted by masses.
What is so satisfying about this, is that all of those orbits neatly fit the numbers from Newton's theory of Gravitation. And they fit the results of Cavendish's experiment as well. They fit so well, that anomalies in observed orbits were used to find previously unknown Uranus, Neptune, and Pluto.
The data very neatly fit the theory. Would you like to see a simple example?