Conventional wisdom still concludes that Galileo’s Leaning Tower of Pisa experiment was correct: that unequal masses free-fall equally. Therefore it should be proper to begin the critique of Galileo’s Leaning Tower experiment by describing how all of the great minds of science down through the ages were understandably fooled by it. And how they attempted to justify, confirm and rationalize such a bizarre, paradoxical, and contradictory result.
Galileo was fooled by his own eyes when he observed two relatively tiny unequal masses fall in apparently equal times toward the relatively enormous mass of the Earth. Galileo thought that he confirmed these early experiments when he determined by trial and error the distance to time ratio for any falling body to be 9.8 m/s/s (Figure 4). He was also fooled by his own eyes when he observed chandeliers and pendulums swing to and fro in apparently equal times, even though he increased or decreased the weights (masses) of the bobs. Galileo merely accepted these paradoxical results as a mysterious law of nature and did not further attempt to scrutinize or explain them.
Newton accepted Galileo’s Leaning Tower of Pisa experiment (and the similar results of others) on face value, in spite of the fact that they directly contradicted his own laws of motion. Thereafter, Newton attempted to analyze, explain and justify Galileo’s Leaning Tower experiment by his own empirical experiments with pendulums. But, unfortunately, such analysis and experiments were ill-conceived and meaningless.
Bessel about 1830, and Eötvös between 1890 and 1909, compared the gravitational accelerations of many small objects, and their masses, substances, compositions and shapes, one against another. After years of such experiments, Bessel and Eötvös concluded from the results of their experiments that the gravitational accelerations (and thus the inertial mass and the passive gravitational mass, i.e. weight, of all these small objects near the Earth’s surface) were equal to a high degree of accuracy. In other words, the Earth’s “downward” pull and gravitational force of attraction acting on each small object (which results in the small object’s phenomenon of heaviness), “is exactly proportional to [the small object’s inertial] mass.” More recently, American physicist Robert Dicke (1916 – 1997) increased the accuracy of these meaningless experiments to “one part in 10,000,000,000.”
By 1915, Einstein was also convinced by the above empirical experiments and statements of equality, and he concluded that gravitational acceleration was truly an absolute concept. On face value, Einstein accepted the results of Galileo’s and Newton’s experiments as natural law:
“…the fundamental property of the gravitational field of giving all bodies the same acceleration, or what comes to the same thing, on the law of equality of inertial and gravitational mass.” 
Thereafter, Einstein premised his entire General Theory of Relativity upon the above invalid and meaningless concepts.