The answer already provided is a good answer, but I would add that speaking of tears as "womanish" reminds one that traditionally, men did not cry;shedding tears was considered a weakness, appropriate only for women. You might also consider that the Friar is momentarily angry with Romeo for suggesting suicide, a mortal sin.
These lines come from Act III, Scene 3. Romeo has killed Tybalt and will be banished from the city. He's talking to Friar Lawrence and The Nurse at this point and has just said that he wants to find out what part of his body makes him a Montague so he can cut it out. He wants to do this because he feels that his family name makes it hard for him and Juliet to be together.
It is at this point that Friar Lawrence speaks the lines you cite. When he does so, he is going on the old idea that women lacked the ability to reason and to think clearly. He is telling Romeo that he is essentially losing it. He's telling Romeo to snap out of it, stop being desperate and like a woman or an animal (like I said, they didn't think much of women's intellectual capacities).
So essentially the Friar is telling Romeo to stand up, be a man, and deal with what's happened.