What trait in Romeo does Friar Lawrence find fault with? What reason does Friar Lawrence give for helping Romeo and Juliet?

Friar Laurence is baffled that Romeo, who only a few days ago claimed he was madly and sadly in love with Rosaline, is now in love with somebody else altogether. Friar Laurence teases Romeo, about how quickly he has changed his mind:

ROM:
Thou chid'st me oft for loving Rosaline.

FRIAR:
For doting, not for loving, pupil mine.

ROM:
And bad'st me bury love.

FRIAR:
                                    Not in a grave
To lay one in, another out to have.

ROM:
I pray thee chide not. She whom I love now
Doth grace for grace and love for love allow.
The other did not so.

FRIAR:
O, she knew well
Thy love did read by rote, and could not spell.

Friar Laurence's real message is in the last line: Romeo's love read by rote (i.e. read by memory) rather than knowing the letters. Romeo, in other words, ain't old enough to understand love yet.

But Friar Laurence, all the same, will agree to marry the two young lovers:

But come, young waverer, come go with me.
In one respect I'll thy assistant be;
For this alliance may so happy prove
To turn your households’ rancour to pure love.

Friar Laurence agrees to marry the two because he believes their "alliance" (their marriage) might heal the "rancour" (anger) of the two households, Montague and Capulet. He thinks the marraige will make the households friends: and he's probably right.

Only, we never get to find out, because, before it is made public, Romeo has murderer Tybalt, and the Capulet-Montague relationship has become somewhat more complex.

Hope it helps!