is central to the plot and themes.  

Amir is a Pashtun, and Hassan is a Hazara.  The Pashtuns are the ruling class in Afghanistan, and it is clear that the Hazaras are a lower class and ethic group, historically treated quite poorly, and also shown as treated quite poorly in the setting of the novel. Hassan and his father Ali are servants in the household of Baba and Amir, and while Amir and Hassan are raised together, there is a clear line in Amir's mind of their differences.  Amir notes,

But in none of his stories did Baba ever refer to Ali as his friend. ... I never thought of Hassan and me as friends either (25).

Amir looks down upon Hassan, and the relationship is such that Hassan saying "For you, a thousand times over" is really what Amir expects from Hassan, because he perceives him to be an inferior servant.  He really does not see that Hassan is a true friend and is saying this out of love, not out of duty as a servant.  

On his long journey of learning and repentance, as Amir finds himself and his father looked down upon in the new land, the shoe is on the other foot. They are subject to small, daily humiliations in the United States, for example, Baba's humiliation at collecting any kind of benefits and Amir's concern about not being quite good enough to wed Soraya, whose father is a general. Amir begins to understand what it feels like to be regarded as inferior.  By the time he rescues Sohrab and says to him, "For you, a thousand times over," this is meant to represent not only his repentance for what he had done to Sohrab's father, but also his understanding that we must all be servants to one another and that class and ethnicity should play no part in our willingness to do so. He is saying this out of love and friendship, as Hassan had said it to him. 

So, while there is no question that the use of this declaration represents Amir's repentance for all he has done wrong to Hassan (and Ali), I do think that the class and ethnic tension are part of the meaning behind its use, too.

The whole theme of The Kite Runner is one of forgiveness and repentance. Amir spends most of the story trying to make up for a wrong he did many years ago. When Amir asks Hassan to run the kite for him, Hassan says "For you, a thousand times over". This one statement will haunt Amir for many years to come. Amir betrays Hassan in the most horrible way possible. When Hassan is running the kite, he ends up in the alley. Assef is there and Hassan tries to confront him. Hassan is outnumbered and Assef rapes him. Meanwhile, Amir is hiding watching this happen. He does nothing to try to help his friend or defend him. This is the major turning point of the story. This is the point when everything changes for all involved.

Years later Amir is still haunted by that one moment in his life. It has haunted him for years. When he learns about Hassan's son, Amir knows what he has to do. He has to try to make up for the injury he caused so many years ago. When Amir takes Hassan's son home with him, the one thing that they have in common is kite flying. The story comes full circle. Amir is finally able to mend some of the hurt he had caused and ease the anger he feels toward himself.

In The Kite Runner, the line "For you, a thousand times over" is explicitly related to the theme of repentence in the novel.  Hassan says this line first in the novel when he runs the kite for Amir.  Readers learn soon after that the running of this kite leads Hassan into the alley where he is raped by Assef.  Amir betrays Hassan in this scene and does nothing to try to help Hassan.  Years later, Amir embarks on a quest to redeem himself from this cowardly act, and he ends up with Hassan's son Sohrab.  Amir tells Sohrab that he will run his kite "a thousand times over" as way to show his repentence.  Amir recalls this line as he attempts to make up for the past.

In Chapter 7, on page 51 of the Riverhead Books Edition of the novel The Kite Runner,Amir tells Hassan to come back with the blue kite. As Hassan is running after the kite, he stops and turns around. Hassan cups his hands to his mouth and says, "For you a thousand times over!" (Hosseini 51). Hassan's response depicts his loyalty, commitment, and love for Amir. Later on in the novel, Amir atones for his past sins by saving Hassan's son, Sohrab, and taking him to America. At the end of the novel, Amir is desperate to have a relationship with Sohrab, and he finally has a breakthrough when he begins to fly a kite during a picnic. Sohrab joins him, and they end up cutting down another person's kite. Amir then asks Sohrab if he wants him to run after the kite. Sohrab nods and Amir says, "For you a thousand times over" (Hosseini 259). Amir's comment also depicts his loyalty and love for Sohrab.

The idea of "For you, a thousand times over" seems to indicate that no matter how many difficulties emerge, the devotion and love one has towards another will always remain.  Certainly, this is true for Hassan and Amir, and ends up becoming true for Amir and Sohrab.  I think that a great work with the poetic quality to capture the devotion in the line would be the Lennon/ McCartney song, "In My Life."  I think that the song does a great job of capturing this devotion to someone throughout one's life.  The song expresses how consciousness can be challenging and divergent, but is seemingly brought into convergence with the idea of devotion towards a particular person.  The idea of change, yet remaining constant towards the element of specific devotion is something that is evidenced in how Hassan is loyal to Amir and how Amir learns to become loyal to Sohrab.  I think that this idea of "for you, a thousand times over" is brought out in the song in that both display how individuals can change without sacrificing their initial devotion and loyalty towards another.  Residing at the core of their being and the center of their consciousness, it becomes evident that "For you, a thousand times over" and "In my life, I've loved you more," are almost interchangeable in meaning and intent.