Based on what we have read so far, it can be said that Amir's sin was that he stood by and watched as Hassan got raped trying to defend the kite which would be the trophy of his victory in the kite fight. Everything he got as a result of the kite made him sick. He threw all of the gifts he received in a pile. He said that he got those gifts through "blood money". It can also be said that amir sinned when he he set up Hassan to get him thrown out and replaced. Hassan ended up confessing to the crime and leaving the house.
Amir has not yet been able to atone for the things he considers his sins and will probably not be able to unless he sees Hassan again.