How do Rosencrantz and Guildenstern show the change Hamlet undergoes and the extent of his paranoia?
When you compare the light joking that opens their first conversation in Act 2 to Hamlet's complete dismissal of their importance as he relates their future deaths in Act 5, it is clear to see that Hamlet has come to a place where he does what he has to do in order to save himself.
When they first meet up in Act 2 Hamlet is guarded (still putting on his crazy act as demonstrated through the use of prose, not verse) but light. He jokes about their "living in Fortune's middle" and speaks in hyperbole about how "Denmark is a prison." But the conversation quickly becomes more serious when Hamlet directly asks them whether they were sent for and the two men don't answer directly. Hamlet seems a bit sad and bit desperate as he begs them to be honest. I don't know that this behavior is paranoia, but he certainly is justified in being suspicious. Hamlet states directly that he knows he can't trust them.
As the play progresses, nothing changes in that regard and, in fact, the two men show that their loyalty is much more clearly tied to Claudius. The whole situation comes to a head when Hamlet discovers the note from Claudius to England that is in their possession. Hamlet realizes that he must take drastic action in order to save himself, so he changes the letter to name the "bearers of this letter" as the ones to be immediately executed. Hamlet can't feel bad about this act -- he has no way of knowing that he would be escaping the boat to England the next day when the pirates attack the ship. He needs to save himself! When Horatio hears the story he is clearly impressed with Hamlet's actions, proclaiming, "Why, what a king is this!" Again, I don't think these actions are a result of paranoia, but are driven by a need to protect himself at all costs.