Being an inhabitant at Versailles meant constant access to the King and thereby power which was so attractive to courtiers that they would happily occupy cramped attic rooms for the privilege. It is quite difficult to imagine lords and ladies usually so meticulous with their rights and dignity cramping themselves into tiny apartments!
As you can see the number of apartments has been considerably reduced from 1732 (directly beneath this text) to 1837:
Luckily this is from 1837 which means that this is how it would have looked like during Louis XVI's reign. The downside of living in one of the otherwise much-sought-after attic apartments was the temperature. During the summer it would be intolerably hot and freezing during the winter.