Gravity provides an acceleration of roughly 9.8m/s2s2.
If you're normal height, something free falling for one second would have to fall about two and a half to three times a person's height. If you're just 1mm tall, the object would fall 4,900 times your height.
Now that ignores drag, etc. But yeah, anything you drop would seem to hit the ground really, really quickly (unless you were somewhere with notably lower gravity than Earth).