Using Act 2, page 61 ("The common room of Proctor's house...") through page 68 line 3 ("Strangely, she doesn't resist him, but hangs limply by his grip."), analyze the scene and pay attention to Proctor's and Elizabeth's relationship.
That's a strange line to pick regarding the analysis of John and Elizabeth's relationship. The reason that I say that is because that line refers to how Mary Warren reacts when John grabs her. John is upset that Mary Warren went into Salem even though he earlier forbade it. John threatens to even whip her. Mary doesn't resist because she is physically and emotionally drained. 39 people have been arrested on suspicion of witchcraft, and Mary is beginning to realize the gravity of the situation that she is a part of. Her non-resistance and limp body indicate that she wants to be done with the trials and return to John and Elizabeth's household.
As for the relationship between John and Elizabeth, it is as strained as it has been for quite some time. It has been 7 months since John and Elizabeth fired Abigail Williams from their house. The termination is a result of John's adultery with Abigail. To be sure, John and Elizabeth's relationship was strained before that. Otherwise John likely would not have committed adultery with Abigail.
John is an honest, good man (despite the affair). He feels horrible that it happened and has a profound sense of guilt about it. At the same time, Elizabeth says that she has forgotten Abigail and forgiven John, which may be true, but she doesn't act like it. Elizabeth has grown more cold and distant from John over the past 7 months.
Proctor, with solemn warning: You will not judge me more, Elizabeth. I have good reason to think before I charge fraud on Abigail, and I will think on it. Let you look to your own im-provement before you go to judge your husband any more. I have forgot Abigail, and -
Elizabeth: And I.
Proctor: Spare me! You forget nothin’ and forgive nothin’. Learn charity, woman. I have gone tiptoe in this house all seven month since she is gone. I have not moved from there to there without I think to please you, and still an everlasting funeral marches round your heart. I cannot speak but I am doubted, every moment judged for lies, as though I come into a court when I come into this house!
Then a few lines later,
Proctor: Let you look sometimes for the goodness in me, and judge me not.
Elizabeth: I do not judge you. The magistrate sits in your heart that judges you. I never thought you but a good man, John - with a smile - only somewhat bewildered.
Proctor, laughing bitterly: Oh, Elizabeth, your justice would freeze beer!
As you can see, John and Elizabeth might be a married couple that live in the same house, but that is all that they are: two people that live in the same house. John's guilt causes him to misinterpret every look and word from Elizabeth, which drives them further apart. Elizabeth's cool aloofness from the situation causes John to think that she has not forgiven him. At this point in the play, their relationship is a hollow shell. They are married before the eyes of the community, but have no real relationship.