Remus let Sirius settle against him however he needed to. He wanted him to be as comfortable as possible, and he wanted to take care of him. He pushed aside his own pain, and did not let his broken heart become a factor. This was about Sirius, and making sure he was all right.
"I'll keep you safe," he whispered, and slipped an arm around his shoulders. He couldn't very well hit Sirius, and couldn't imagine himself ever hexing him. But he'd find a way to keep him from slipping, so long as he was there.