The metal weights were dense enough that gravity overwhelmed air resistance. Galileo was performing an experiment about gravity. Air resistance was merely a small complication which could be ignored. Astronauts on the moon performed this experiment, and the feather fell at the same rate as a metal weight. Actually, that experiment has been performed thousands of times, by students, in partial vacuums here on earth.
Some people criticize the formulas and laws of physics, for applying only to idealized conditions.
Well, a formula or physical law which takes into account all possible forces, is often so complicated that it becomes useless. Instead, you start with the simple law, like galileo's hypothesis above, and then make small corrections for the outside forces, if you have to. Then, you get a much more basic understanding of the principles involved. But he never claimed to have performed it. Had he actually performed the experiment, it is likely that he would have reported that.