After Amir wins the Kite Tournament, He sees his son in a better light and is proud of his son for once. Before the tournament, he was always worried about Amir not fitting to the stereotypical mans role, especially as a Pashtun. This is because Amir wasn't very strong, didn't stand up for himself, and he wasn't very interested in football. Because of this, Baba never felt like he could relate to Amir which affected their relationship. However, after the tournament, Baba gains more faith for his son.
In the move to the US, Amir and his father have more alike, Amir isn't actively seeking approval as they are barely surviving. Amir starts becoming a man and all grown up which strengthens the bond between father and son.
In America, how Baba's character is viewed also changes because in Kabul, he was in the majority and among the highest class. However, there is no caste system in America as well as the fact that nobody in America knows who he is. In Kabul, he was known for being successful and rich but in America, he was essentially a nobody.