If a balloon were floating next to the International Space Station (ISS), how big, light, and/or dense would it need to be such that the gas/atmosphere at that distance from the earth's surface would cause it to visibly accelerate relative to the ISS? I'll say provisionally that the acceleration would need to be at least $10^{-3}\text{ m }\text{s}^{-2}$.
I looked all over just now, trying to find out what the density of the atmosphere is at $400\text{ km}$ but all I could find were figures for the lower atmosphere, and for the thermosphere, which is what the ISS orbits inside, log graphs that I can't decipher and equations that I am not smart enough to be able to use.
https://space.stackexchange.com/a/38130/40252 has a graph (is it reliable?) which if accurate implies that the density at four hundred kilometers is about one trillionth of a kilogram per cubic meter. This figure is conveniently a round number, and is close to one trillionth of the density of air at sea level (Wikipedia says: At $101.325$ kPa (abs) and $15$°C, air has a density of approximately $1.225$ kg m$^{-3}$.)