To make a cookie airy, make sure you cream the butter first for 2 minutes. Also, chilling the cookie dough for about 15 minutes will also make them airy. "Folding" the cookie dough using a silicone spatula will also make the cookie airy. Instead of using a stand-alone mixture, use the spatula to fold in the butters, sugars and flour. This will incorporate "air" into the dough.