na-adjective
self-important; pompous; conceited
Describes someone acting as if they are superior or more important than others; often used critically.
彼はいつも偉そうな態度をとる。
He always acts self-important.
あの先生は偉そうに話すから、あまり好きじゃない。
That teacher talks pompously, so I don't like him much.
威張る is a verb meaning 'to act bossy' or 'to throw one's weight around'; 偉そう is an adjective describing the appearance or manner.
Derived from 偉い (great, superior) + そう (seems, looks like). The combination literally means 'seems great' and is used to describe someone who acts as if they are important.