Why does moist air naturally float into the attic?

It comes down to air temperature and whether the air is dry.

At the same temperature, a column of dry air will be denser or heavier than a column of air containing any water vapor. Thus, any volume of dry air will sink if placed in a larger volume of moist air. Also, a volume of moist air will rise or be buoyant if placed in a larger region of dry air. As the temperature rises the proportion of water vapor in the air increases, and its buoyancy will increase.