Before Sirius had much time to cross the room, or even to properly react to how sodding happy he'd just seen them look, he found himself with an armful of his baby cousin. (Inwardly, Sirius shuttered at the title.) He was still for a second, everything in his chest and mind telling him he couldn't possibly hug back, that really, he should be shoving her away. He couldn't have even missed her, right? To him, he'd just seen her.
So he couldn't really explain why he let his arms go around her, even briefly.
Later he might have denied it, but in that moment, the answer was probably that he bloody needed it. And somewhere in that half-second, he'd accepted that. Then he glanced up at Remus over her shoulder, and let her go. "Yeah, well. Don't blame you, s'a nice face."
It was a typical Sirius Black response, if not said entirely in a Sirius Black sort of way.