Sirius saw that smile and his heart melted as he swayed unconsciously toward Remus, following him instinctively. His heart was much lighter now, despite the whole having to apologize to Severus thing. But if he were to be honest with himself - and he was capable of doing that when he truly tried - he hadn't meant to kill Snape, just scare him, so he was being truthful in his apology, even if he wasn't sorry that Snape was unscathed, at least physically. He couldn't lie about that much - he did hate Snape. Very much. But whatever.
He followed Remus obediently, and once they were out of the stands, they were able to walk two abreast once again. Sirius didn't try to keep up a conversation for once. He was just grateful that they were talking again at all, the past week had been sheer torture. The worst he thought he'd ever endured. It was a companionable silence. Now and then Sirius brushed against Remus "by accident", as if to assure himself that he was really there.
Once they reached the school, he allowed Remus to take the lead, just in case he'd changed his mind about going to the library right now, although he suspected that he hadn't.