Pohnpei is right... if you look at Act III, scene i, you will find that Mercutio criticizes Benvolio for being ready to fight over just about anything, including a person having a hair more or a hair less in their beards, wearing their Easter outfit before Easter, tying old shoes with new ribbons.
Benvolio defends himself and asks if he is such a fellow. I think we can logically assume since Mercutio likes to hear himself talk, that this phrase within that group of phrases was intended to demonstrate that Benvolio fights over nothing... but the truth is Benvolio is not a fighter.
I do not believe that this phrase appears in Romeo and Juliet at all, and I particularly do not think it appears in this scene.
In this scene, the character Peter uses the word "quarrel" but he does not use it in anything like the phrase you mention.
I thought that maybe you were referring to a part in Act III, Scene 1 where Mercutio is telling Benvolio that Benvolio is always ready to quarrel. Your phrase would fit there, but it's not there.
I would think what the phrase would mean is that the person is ready to fight over any little thing. It would mean that even more if it were "ready to quarrel over a trifle."