In these lines, Juliet displays her lack of understanding of the affairs of the heart. Lady Capulet is determined that her daughter should get married to Paris, a young man from a very good family. She puts Juliet on the spot, demanding that she give a quick answer to the question, “Can you like of Paris, love?” In other words, Lady Capulet wants to know if Juliet can accept Paris' love.
In reply, Juliet says that she will look at him and try to like him, providing of course that what she sees is likable. But even if she does find him likable, Juliet says that she won't allow herself to fall for Paris more than her mother's permission allows.
In her innocence and lack of experience, Juliet seems to think that you can simply determine your feelings for someone in advance and that you can control how you'll react to someone before you've even had the chance to meet them.
What this shows quite clearly is that Juliet doesn't yet understand what love is or how it can take hold of one's emotions. It's fair to say that if Juliet had fallen head over heels in love with Paris, then she would've found it as hard to keep her emotions in check as she does when she falls for Romeo.
Juliet will soon being seeing Paris for the first time at the masquerade ball the Capulets are holding. Paris has asked Lord Capulet for Juliet's hand in marriage. While Lord Capulet thinks it is too early for Juliet to marry, as she is not quite fourteen, both parents think it is a suitable match.
Therefore, Lady Capulet comes to Juliet's chambers to introduce to her the idea of marrying Paris. She sings Paris's praises: he is good looking, he is rich, people would admire you for marrying him, he would be a a fine match. She ends by asking Juliet if she can "like" Paris.
Juliet responds with the quote above. She says in the first line that she will look at him with the idea of liking him, if he is likable. In other words, she will go to the party with an open mind and positive attitude, trying to see the good in Paris if at all possible. In the second line, she says she won't love any more than her mother allows: by saying "endart my eye" and "make it fly," she refers to Cupid's arrow. She assures her mother she won't fall in love more passionately than her mother would like.
All of this shows that, in contrast to the lovesick Romeo, Juliet is not in love and has no idea what it means to be in love: she does not yet know it is not something she cannot control.
Romeo and Juliet tells the ageless story of the two "star-crossed" young lovers, a story which has inspired many and which is doomed even before the two meet, as the "ancient grudge" between their families promises certain destruction.
Having reached an age when marriage is a potential topic of conversation for Juliet's parents, Juliet is not interested in any such discussion. Even her father admits to Paris that he would prefer to wait two more years before he would consider Juliet to be of an age to marry. He says, "Let two more summers wither in their pride" in Act I, scene ii, line 10. Having suggested that Paris therefore takes his time, Capulet cautions him to "get her heart" (17), accepting that even his own consent to marry Paris is reliant on Juliet's own agreement. He does add "within her scope of choice" in line 18 which is significant because later he will insist that she marry Paris (immediately) and this fact will drive Juliet to extreme action. It seems that Juliet does have some measure of independent choice as long as her choice is reasonable to her parents. Juliet, however, has other ideas about the extent of her independence.
Shortly after Paris's discussion with Capulet, Lady Capulet discusses Paris's intentions with Juliet in Act I, scene iii. Lady Capulet wants Juliet to consider Paris's proposal and she wants her to use the feast as an opportunity to find out more about him. This is when Juliet offers to "look to like..." (98). Juliet is appeasing her mother by agreeing to think over the matter. She will observe him "if looking liking move," meaning if her mother thinks that that will make any difference. Juliet goes on to say that "no more deep will I endart mine eye" meaning that she will not go to any extraordinary measures to make herself like him. When she finishes off with "than your consent gives strength to make it fly" she is suggesting that her mother's encouragement is not having that much effect in persuading Juliet to favor Paris anyway. She still does not want to get married at this point.
Here is a paraphrase of Juliet's words to her mother when she has been asked if she could possibly love Paris, whom she is about to meet: I will look at Paris tonight and see if I feel any chemistry with him. And even if I do, I won't go overboard without your consent.
Isn't she an obedient child? Shakespeare needs to portray her this way so we can see what a change she makes once she really feels chemistry with Romeo. In essence, Juliet is allowing her mother final say in who she will love....not long after meeting Romeo, she refuses to allow her parents to dictate her fate.
The image of the arrow (endart, fly) is often used when people fall in love...an allusion to Eros (Cupid) and his arrows.