Gravity affects pressure affects density. To a first approximation, gases have density directly proportional to their pressure, and liquids and solids don't compress very much.

With air/water/pen the conclusion doesn't change. But an example where it does:
A nitrogen atmosphere at STP has a density of 1251 g/m^3.
A helium balloon at STP has a density of 179 g/m^3. The balloon floats.
Then reduce Earth's gravity by a factor of 10, and hold temperature constant.
The atmospheric pressure reduces by a factor of 10, so its density goes to 125 g/m^3.
But the helium can't expand likewise (assume the balloon is perfectly inelastic), so it's still 179 g/m^3. The balloon sinks.