Nurse is annoyed at Romeo because he does not interfere when Mercuito is teasing her with bawdy jokes, and because he weeps for Juliet.
Romeo and Nurse’s relationship is an interesting one, because she is one of the few people who actually knows what is going on. She is irritated with him several times. Nurse is first annoyed at Romeo because he has eyes for Juliet, and then because he secretly marries her when Paris is a much better catch. However, the time when she yells at Romeo because Mercutio was teasing her is the only time she is really angry at him.
In Act 1, scene 5, Romeo crashes Juliet’s party at the Capulet house. He is caught by Tybalt, who wants to start a fight, but her father lets him stay. Then, Romeo sees Juliet and they talk, and then kiss. At this point, the nurse intervenes by telling Juliet that her mother wants her. Romeo asks the nurse who she is, and finds out she is a Capulet and the daughter of the house.
I tell you, he that can lay hold of her
Shall have the chinks. (Act 1, Scene 5, p. 33)
She tells Romeo that whoever marries Juliet will have money, but then Juliet asks her his name, nurse replies that he is “the only son of your great enemy” (Act 1, Scene 5, p. 34). Juliet then denies that she is interested in Romeo.
Unfortunately, Romeo’s friend Mercuito annoys Nurse by teasing her. She asks Romeo about his “saucy” friend and he laughs it off by saying that Mercutio just likes to hear himself talk.
Before she tells him she is a messenger from Juliet, she is annoyed at Romeo because she has been annoyed at Mercuito, and the servant Peter. Romeo basically gets her on a bad day. She grumps at him.
And thou must stand by too, and suffer every knave to use me
at his pleasure! (Act 2, Scene 4, p. 53)
She is annoyed that he just stood there and did not interfere in Mercutio’s teasing or jump to her honor.
When she finds Romeo crying about being banished, she gets a little miffed as well. She finds him blubbering on the ground with Friar Lawrence.
Stand up, stand up! Stand, an you be a man.
For Juliet's sake, for her sake, rise and stand!
Why should you fall into so deep an O? (Act 3, Scene 3, p. 71)
By this point, Nurse has taken on Romeo as another one of her charges. She cares about him, for Juliet’s sake. She wants him to be a man, for her, and stand up for her both literally and figuratively as a good husband.