As the story takes a philosophical turn in the previous verse, Matthew 22:11, that tone continues here, ending on one of Jesus's statements that are exaggerated for humor.
Jesus uses the phrase "weeping and gnashing of teeth" in the same humorous way that we say in English "whining and complaining" or "bitching and moaning." The "gnashing of teeth" could indicate the chattering of teeth, conveying the sense that this person is tossed out "in the cold," except that Jesus uses this same phrase earlier to describe weeds cast in a fire.
Christ's Words in Matthew as a Guide to 40 Days of Prayer.