How does Catherine's character develop in A View from the Bridge?

At the very beginning of the play, Catherine is like a young child craving her uncle Eddie Carbone’s approval. She asks him three times in quick succession, “You like it?” about her outfit and her hair. She is insecure and needs his approval to validate her looks and her abilities.

Eddie is overprotective of Catherine, whose mother has died, and he is jealous. He does not want her “walkin’ wavy,” which means he thinks she is too provocative, and says, “I don’t like the looks they’re givin’ you in the candy store.” The stage direction says, “Catherine (almost in tears because he disapproves), [asks] 'What do you want me to do?'” At this early point in the play, Catherine does not rebel against Eddie. She is too timid and fears him.

For instance, when she and Beatrice tell Eddie that Catherine has been offered a new job, he insists that she complete school first. She protests gently and states her point of view but is not insistent about it. When Eddie finally relents and tells her to accept the job, she nearly breaks into tears in relief. She does not want to defy him, and she needs him to approve her choices.

Over the course of the play, Catherine grows to resent Eddie’s babying her. When he chastises her in front of Marco and Rodolfo, the stage direction states, “Embarrassed now, angered, Catherine goes out into the bed room.” She does not want him to treat her like a baby in front of the two men, although she is still compliant. At his direction, she changes her shoes.

Rodolfo comments that it is almost as if Catherine is afraid of Eddie and Beatrice tells her that she acts like a baby with Eddie:

Catherine: Yeah, but how am I going to do that? He thinks I’m a baby.

Beatrice: Because you think you’re a baby. I told you fifty times already, you can’t act the way you act. You still walk around in front of him in your slip—

Her attitude towards Eddie begins to change as she realizes her own inner strength and her adult needs and wants. She speaks to him “with an edge of anger.” When Eddie asks if she likes Rodolfo, she responds, “holding her ground.” Finally, when Eddie tries to shake her love for Rodolfo, she yells, “I don’t believe it and I wish to hell you’d stop it!”

The more compliant Catherine at the beginning of the play would never have spoken to Eddie this way, but she has become more independent and self-assured.

By the end of the play, she breaks free of Eddie and tells him, “I’m gonna get married, Eddie. So if you wanna come, the wedding be on Saturday.” She does not ask his permission; she states her plans with no care if he approves or not. Finally, she tells Marco:

To hell with Eddie. Nobody is gonna talk to him again if he lives to a hundred. Everybody knows you spit in his face, that’s enough, isn’t it? Give me the satisfaction—I want you at the wedding.

How does Catherine contribute to Eddie's downfall in A View From the Bridge?

To a large extent, Eddie's feelings for Catherine, or Katie as he always calls her, are directly responsible for his downfall. For one thing, he's overprotective towards her. He puts Catherine on a pedestal; to him, she's a Madonna-like figure—virginal, chaste, and pure. Eddie thinks the big old world outside is no place for such an innocent young lady, and he vows to protect her come what may, determined to live up to the promise he made to Catherine's mother on her deathbed.

Because he's so overprotective, Eddie is strongly opposed to Catherine going on dates. Men will take advantage of her innocence, he thinks; but by keeping her all cooped-up at home where he can keep an eye on her, he's making it harder for Catherine to lead any kind of life out there in the real world. Nevertheless, Eddie can't prevent the world outside from entering the confines of his home, no matter how hard he tries. For when Marco and Rodolpho come to stay, Eddie's whole world starts to collapse, and with it the control he's exercised over Catherine's life.

Eddie senses that he's losing Catherine to Rodolpho. This makes him ever more desperate to win her back. It's too late, however; Catherine's growing into a woman, capable of making her own decisions in life. She's finally able to break free from Eddie's stifling control, which never allowed her to develop properly. Eddie is so set in his ways, so used to getting what he wants, that he can't face the changing reality. He resorts to desperate measures to drive a wedge between Rodolpho and Catherine, calling the immigration department to try and get Rodolpho and Marco deported back to Italy.

Despite her growing maturity, Catherine still feels guilty at Eddie's death, that she's somehow responsible for what happened. It would be more accurate, however, to say that it is Eddie's uncontrollable feelings for Catherine that cause his destruction, rather than Catherine herself.