Why do the Friar and Nurse, adults who care deeply about the young lovers, allow them to act so quickly on their feelings? (support your answer...

The Friar's reason for encouraging the lovers to move forward so quickly with their relationship is somewhat easier to explain.  When Romeo comes to tell Friar Lawrence about his desire to marry Juliet, the daughter of his father's enemy, the Friar eventually agrees to perform the ceremony because, as he says, "this alliance may so happy prove / To turn your households' rancor to pure love" (2.3.98-99).  In other words, he hopes that the joining of these two young people in marriage will compel their families to put aside their grudge and cease their violent feuding.

Juliet's Nurse, on a different note, simply seems to think that her young mistress is ready to marry.  When Lady Capulet comes to acquaint her daughter and the Nurse with the Count Paris's desire to marry Juliet, the Nurse gets really excited and eventually tells Juliet, "Go, girl, seek happy nights to happy days" (1.3.113).  She seems to think that marriage will make Juliet happy, and so she supports Juliet's desire to marry Romeo, especially because he is so handsome and honest.  Further, she seems to want Juliet to hurry up and have kids!  She makes jokes about how "Women grow by men" (1.4.101), and almost the first thing she says after she tells Juliet the plan to get her married that day is how she has to go find a ladder so that Romeo can climb up to Juliet's room and she can "bear the burden" of him (2.5.81).  In any case, the Nurse alludes to sex and/or its effects so often that it seems that she is anxious for Juliet to begin her own family.