You'll most often see this word paring in the idiom whisper empty nothings, which A Dictionary of Cliches by Eric Partridge defines this as meaning "Trivial or superficial remarks, empty compliments …" The concept here is that both words indicate that there is not very much substance to whatever is being whispered. The American Dictionary of the English Language by Noah Webster, which was first published in 1828, even defines airy as meaning:
4. Light as air; resembling air; thin; unsubstantial; without solidity; as, airy ghosts. An airy dress is one which admits air, and is cool.Unfortunately I lack as clear of a reference for nothing, but I doubt I should need it when you consider that the whisperings are being analogized to it.
5. Without reality; having no solid foundation; vain; trifling; as, an airy scheme; airy notions.
Airy nothings are used to curry favor with people for all the same reasons you might usually wish to curry favor with them, although it especially applies to swindling and the seduction of women as is exemplified by this quotation from the [Sunday] Journal, Volume 52, Number 96,Indianapolis, Marion County, 6 April 1902:
He was a superb courtier. He could whisper airy nothings with a grace of gesture and an eloquence of tongue which captivated women and made men envious. It was said of him that during his whole twenty years in Washington he never had to pay for his dinner. He was one of the public men who did not bring his wife to Washington. There are others.I somehow doubt that the intention is to portray Dr. Hu with such a bad character though, so much as it is to suggest that he is just a little too liberal with his compliments for them to mean as much as they might if they came from somebody who exercised some more cautious discrimination with his praise.