to put on airs or give oneself airs: Fig. to act better than one really is; to pretend to be good or to be superior; to consider oneself above others; displaying arrogance.
What a jerk! Why give oneself airs? She's no better than any of us.
When you'll get enough of giving yourself airs and talking nonsense, the rest of us little people can carry on with the meeting.
If someone is complaining, making an unnecessary fuss, or bothering you - you would say "Give over", used in a playful sense - i.e. with friends, kids or pets.