Looking up at Juliet's balcony, Romeo asks, "But soft, what light through yonder window breaks? / It is the East, and Juliet is the sun" (2.2.2-3). This metaphor, comparing Juliet to the sun, shows just how important she has already become to him, how intense his love for her is. We need the sun in order to survive; it makes human life possible. Therefore, Romeo equates her with one of the most vital necessities we have; it is as though he requires her to live -- this is how strong his love feels already.
Later, when Juliet sends her nurse to Romeo after he's been banished for slaying her cousin, Tybalt, she says, "Give this ring to my true knight / And bid him come to take his last farewell" (3.3.155-156). Despite the fact that he has murdered Tybalt, Juliet's love for him remains strong. In fact, she sends a ring to help lift his spirits, and she calls him her "true knight," implying that she only sees him as chivalrous and virtuous and good. Her love is so intense that even Romeo's terrible error in judgment cannot damage it.
In Juliet's tomb, believing her to be dead, Romeo says, "Shall I believe / That unsubstantial death is amorous, / And that the lean abhorred monster keeps / Thee here in dark to be his paramour? / For fear of that I still will stay with thee / And never from this palace of dim night / Depart again" (5.3.102-107). Romeo's love of Juliet is so strong that he doesn't even want her to exist in death without him. If she is dead, then he wants to be dead too. It is as though he would protect her no matter what, and so he must stay with her forever -- whether in life or in death. Their love is so intense that neither one can conceive of a life without the other.