give yourself airs act pretentiously or snobbishly.

☞ Air in the sense of 'an affected manner' has been current since the mid 17th century; from the early 18th century the plural form has been more usual in this derogatory sense.

1948Christopher BushThe Case of the Second Chance It was said she gave herself airs, and it was also hinted that she was no better-as they say-than she might be.