From the second Palamon and Arcite lay eyes on the lovely Emily, they are pierced to the heart by a love so intense that it literally makes them ill. Yeah, they seem like drama queens, but their behavior is pretty typical of the courtly love genre. Palamon and Arcite, two noble knights, spend most of their time pining for the love of a beautiful but distant noblewoman. The knights express their love in terms of wounds and sickness. Emily, the noblewoman, becomes almost a goddess. Palamon and Arcite swear to do anything to win the love of Emily, even if it includes breaking their knights' oaths to protect one another.
But then Duke Theseus comes onto the scene and calls into question this kind of intense love and devotion. Theseus questions why anyone would want to serve the god of love if the only reward for this service is suffering. In the end, though, Theseus admits that he's done some pretty stupid things for the sake of love too. In fact, being lovesick and silly is something all people experience. The depictions of suffering for love that Theseus orders painted in the Temple of Venus prove his point, tying the suffering of Palamon, Arcite, and all lovers to a long and storied history of love.
In "The Knight's Tale," Palamon and Arcite prove the depth of their love for Emily by what they're willing to suffer in order to win her.
Love poses a threat to Theseus's authority because of its ability to trump all other laws.