I would actually argue that Nurse does not evolve as a character. She is recognizably a static character, a character that does not grow or change through undergoing self-revelations due to story development. Nurse is recognized as one of Shakespeare's best comic characters. In fact, she is one character that makes this play a cross between a tragedy and a comedy because it is characteristic of comedies to have a comic female companion; nurse serves as that comic female companion.
Nurse's one and only motivation throughout the play is to make Juliet happy. Juliet's happiness is the reason she agrees to venture out to meet Romeo the morning after the ball and find out if he is truly intending to marry Juliet. We see her ask Romeo what his intentions when she says:
If ye should lead her into a fool's paradise, as they say, it were a very gross kind of behaviour ... for the gentle woman is young. (II.iv.152-154)
Since marrying Romeo makes Juliet happy, she agrees to help them with the marriage and keep it a secret. Later in the play we see her believe that, since Romeo has been banished, marrying Paris would make her happy instead. Hence, we see her recommend that Juliet marry Paris as well, even though polygamy is a sin, which is a very comical suggestion. We see her recommend Paris in the lines:
I think it best you married with the County.
O, he's a lovely gentleman!
Romeo's a dishclout to him. (III.v.227-229)
While it seems from this passage and earlier behavior that Nurse has changed her mind about Romeo and now believes that he is of questionable character due to his murdering Tybalt, we still see Nurse bring Romeo to Juliet, even after his banishment. Hence, we can legitimately say that every decision Nurse makes is for Juliet's happiness alone. While Nurse may change her mind, she does not change her values as a character; she only values Juliet and everything she does is to make her happy. Therefore, we can easily argue that Nurse does not develop as a character throughout the story. She is a static character.
The nurse's character evolves because of Juliet and Romeo's love for each other. The nurse only reluctantly consented to their marriage if asked she might've told the truth about their marriage. Also you can tell she gets more 'pushy' later on when Romeo gets banished, it's almost as if the Nurse is totally fed up with the whole thing because she wants Juliet to marry Paris.