Does less gravity means less air density? I have actually two different questions that may result in the same answer. 
The first one : if the Earth would have less gravity, would it result in less air density?
The second one : On a different planet, let's say on Uranus which is bigger than Earth, the gravity is less than 1g but does that automatically mean that the density of the air is less? Or in some circumstances it can behave the opposite?
 A: Uranus is bigger than Earth but its surface gravity is less. Uranus is made up of gases and is not solid like Earth. This makes Uranus very light for its size so if your talking about at the surface then the density would be less (apples for apples atmospheres). Yes to your first question.
A: Yes. 
Less gravity implies less pressure because the gravity "pulls" the air to the surface of the Earth. And less pressure implies more volume. Ergo, the density of the gases on the atmosphere are less with the new atmosphere pressure.
And your second question, the answer is no. It depends of  chemical composition (as someone commented above). What we call air, here in the Earth is not the same that the Uranus people call air.
A: 
Does less gravity means less air density?

Yes, but only if all other things are equal (same atmospheric mass, same atmospheric composition, and same atmospheric surface temperature). However, all other things are never equal.
Venus, for example, has slightly less mass and a slightly smaller surface gravity than does the Earth (81% Earth masses, 90% Earth surface gravity). Venus's atmosphere, on the other hand, has a surface pressure and density that are much greater than those of the Earth: The surface pressure and surface density of Venus's atmosphere are 90 and 55 times that of Earth's atmosphere, respectively.
