It has less to do with actual weight and more to do with density, and in the case of a feather, air resistance. Droplets are made of mostly water. Water is dense compared to air and will fall through it rather quickly. A feather is not only less dense, it is also designed by nature to offer as much wind resistance as possible, thus, it doesn’t fall through the air quickly.
If the droplets are *very* small (aerosols), they can hang in still air for a very long time. Feathers will drop much faster in the same situation but if there is enough airflow, they can fly around for a long time. Of course, in *that* situation, the germs would not be hanging around because the same air pushing the feathers would push the germs.
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