The Collaborative International Dictionary of English v.0.48:

Airiness \Air"i*ness\, n.
   1. The state or quality of being airy; openness or exposure
      to the air; as, the airiness of a country seat.
      [1913 Webster]

   2. Lightness of spirits; gayety; levity; as, the airiness of
      young persons.
      [1913 Webster]

WordNet (r) 3.0 (2006):

airiness
    n 1: the property of something spacious and abounding in fresh
         air
    2: the property of something weightless and insubstantial [syn:
       airiness, buoyancy]
    3: lightness in movement or manner [syn: airiness, delicacy]