Before Marco and Rodolfo arrive, we see the true colours of Eddie and Catherine’s relationship.
What Miller so perfectly portrays is Catherine’s utter obedience and submissiveness towards Eddie.Her submissive attitude is shown when Eddie asks her to turn around to ‘see in the back’ and the stage direction is “she turns for him”. This happens at the start of act one and already displays the control he has over her. Furthermore, her obedience is shown when “she gets a cigar for him” and even lights it. What is happening at this point is also Beatrice and Eddie being in different minds about Catherine taking the job at the plumbing company, so Catherine is almost filling a sort of wife-like role; doing something like fetching a cigar and lighting it, when Eddie is perfectly capable of doing that himself. She seems to know when he wants something without him even saying anything.
Eddie’s control is portrayed again when he doesn’t want Catherine to take the job because it is in a bad part of town where men, particularly longshoremen (which he ironically is too) will take advantage of her. It’s clear that the idea of other men coming into Catherine’s life is a prospect which brings fear to his, as they might hurt her, but most importantly take her away from his grasp.
Another theme explored by Miller is Catherine’s search of approval from Eddie; it is of great importance that he does approve of her actions and decisions. And when Eddie condemns the way she walks (“wavy”) in her dress, getting the heads to turn like “windmills”, she is “almost in tears because he disapproves”. This could underline the intimacy of what their relationship is, as well as the importance of Eddie’s positive opinions to her.
The comment from Eddie “You ain’t all the girls” shows how precious she is to him, his protectiveness and also the purely taboo nature of their relationship; out of “all the girls” his niece was “the one”.