How is Friar Lawrence's character developed in Act III of Romeo and Juliet?

In Act III of Romeo and Juliet, Friar Lawrence becomes very involved with the fate of Romeo and Juliet; his well-meaning efforts evince his kindness, a certain wisdom, but also frustration.

In Scene 3, Romeo comes to Friar Lawrence in his despair after having killed Tybalt. The Friar tells Romeo that the Prince has fortunately changed his sentence to banishment, rather than death. But Romeo will not be comforted. This reaction of Romeo raises the ire of the priest, and he scolds Romeo:

O deadly sin! o rude unthankfulness!
Thy fault our law calls death; but the kind Prince,
Taking thy part, hath rush'd aside the law. (3.3.25-28)

However, Romeo is not comforted by being merely banished. Friar Lawrence then suggests that he be philosophical about the matter--

I'll give thee armour to keep off that word;
Adversity's sweet milk, philosophy,
To comfort thee, though thou art banished. (3.3.55-57)

but again Romeo will not be consoled, telling the priest that being philosophical will not help him and that Friar Lawrence just does not understand.

Frustrated, Friar Lawrence scolds Romeo, but he still tries to comfort him with the fact that both he and Juliet are alive. Further, he instructs Romeo to be with his wife, but to make certain he is gone by dawn and on his way to Mantua where he will send messages to him.

There is no doubt that Friar Lawrence is a kind, loving, religious man. Perhaps, although he wisely advises Romeo against being so emotional, he takes upon himself more than he can practically handle and, therefore, is frustrated.