Marlow represents the id (impulsive forces, sexual desire for lower class women) and the super-ego (restrained behaviour that is socially acceptable within the upper classes)
Kate functions as a balance between the id and the super-ego of Marlow by helping him regulate the opposite demands of these two forces. Therefore, she exercisestheego in Freudian terms in Goldsmith's play.
Kate, according to Freudian theory, has a deep desire to please her father.
Mrs Hardcastle's lack of involvement with Kate can be interpreted as jealousy of the close relationship between Kate and her father.
Tony represents the id - his actions are governed by what he wants to do instead of what he should do.
Goldsmith's personal experience of being judged because of his appearance may have inspired him to write about appearances being deceptive.
Tony's behaviour could be explained by the lack of a strong father figure to guide him.