The difference in relative acceleration implied by the meme is on the order of tens of yoctometres (10⁻²³ m) per second per second.

It's a difference so small that it would be overshadowed by the fact that you're holding one object femtometres (10⁻¹⁵ m) higher or lower than the other in the gravitational field.

Additional sources of error to consider at this scale might be the heat radiation from the surroundings providing radiation pressure on the object, the sloshing of Earth's core causing time-dependent variations in the gravitational field, the location-dependent variations in the Earth's gravitational field, and the difference in centrifugal (yes, centrifugal in this reference frame) force due to latitude differences of one micrometre, and also due to natural variations in the rate of Earth's rotation over time.