High atmospheric density
As pointed out in the comments by @M I ech, gravity and gas mixing has little to do with it.
Heavier than air craft, as in airplanes and helicopters, rely on lift to get off the ground and stay aloft. Lift is created by creating a disparity between the air pressure above the lift surface (wing) and the air pressure below the lift surface. So when the air pressure above the wing is lower than that below the wing then craft is capable of moving upwards. See the Wikipedia entry on lift for more info.
Increasing the atmospheric density would create a higher standard pressure, and therefore make it easier for a heavier-than-air craft to create the needed pressure differential for take off. Incidentally, this is the same situation (but reversed) that requires hypothetical Martian aircraft to be light with large wings.
As for lighter than air craft, like blimps etc, this problem becomes exceedingly easy. Lighter-than-air craft rely on the same principle of buoyancy as boats: by introducing a large volume with a lower density than the medium (air or water) then you can decrease the average density of the craft and it floats. In a situation where the surrounding air is denser, this again means that it is easier to create a volume of lower density and take off.
This is of course assuming a) gravity on the order of 1G (different gravity will have other effects on these forces) and b) hand-wavey sci-fi tech like inertial dampeners or anti-gravity are not options.