Disclaimer: These characters do not belong to me.
Sirius did not grow up hating his family (nor did he come out of the womb doing so, as he later told it). It wasn't quite possible for him to do that. They were his family. His cousins watched over him in their cool manner, and his brother was a little bit dribbly until he turned four and thought that Sirius was the best thing to ever walk the planet. And his mum never beat him or anything. She was a harsh, yes, and dignified and exacting, and maybe she didn't give hugs like James' mum did, but she wasn't—she was—well. She was his mum.
He didn't meet James on the Hogwarts Express, and they weren't best friends from the start. He actually met James when the two of them were five and his mum told them to go play, because the Potters may have been blood-traitors, but they were blood-traitors with Connections, and they came from Old Money. (When Sirius told James this, James looked confused and said that they got their money from Gringotts just like everyone else, so what was so special about that anyway?)
Sirius didn't ask for Gryffindor, and the Hat didn't put him there the moment it touched his head. Sirius was torn. Sirius knew that he would hate it in Slytherin, with their rules and their power games and everything that seemed like what he hated about home. (Gryffindor, then, my boy?) Sirius was eleven, and just didn't want to disappoint his family. (Or perhaps not). Sirius was torn. (There's no lack of courage in you, but you also know to be ruthless when you have to). Sirius just wanted the choice made for him. (I'm afraid the world will need your bravery, my boy. GRYFFINDOR!)
Sirius and Remus were never anything more than friends. Oh, he wanted to, he wanted so much it hurt, but he was scared. (Some Gryffindor you are). He was scared, and then there was a war, and then Azkaban, and then Sirius knew that all he had was Remus, and one wrong word could break all that, so he kept silent, like he had kept silent for the last twenty years. And he lived his next two years always in fear of that one wrong word, until he fell through the Veil, and met Remus' eyes, and knew that any word he might have said would have been the right one.
Sirius never thought Harry to be anyone other than who he was. There were moments that might have seemed otherwise, sharp moments he wished he could have taken back, but when he looked at Harry he never saw James. He saw only a boy that James would have been so proud of. A boy James would have been so proud to have raised.
When Sirius fell through the Veil, after Remus, he thought of Bellatrix. Bellatrix, Bella, his cousin, her mind snapped from the horror he knew all too well. His cousin who had come home from Hogwarts one day when he was seven and handed him her wand. Here, she had said. I'll show you how to curse anyone who tries to hurt you. You are a Black, and we take care of our own. Bellatrix who he hated and who hated him, but could only hate him so fiercely because they had loved one another once.
It didn't hurt him to watch Remus and Tonks from above. It would have hurt him to see Remus alone, alone on moon nights, healing himself alone, living with his books and his tea and silence. Blacks took care of their own, and Tonks had Black blood in her veins. She had made Remus her own, and she would take care of him.
It was quiet in the afterlife. James and Lily were there, and sometimes the three of them would walk the streets in a comfortable silence. Sometimes they would reminisce; sometimes they would watch down below. They were waiting. (They'll join us soon, James said, arm around Sirius' shoulders. Hopefully not too soon, Sirius replied, eyes fixed downward). It was quiet in the afterlife, and Sirius couldn't remember ever being happier.