The entire situation was scaring the hell out of Remus. He didn't know how much more of this he could really take before he fell to pieces. He loved Sirius more than anyone or anything in the world, and seeing him this way was killing him. He could only imagine what it was doing to Sirius himself. He could understand now why he was so disturbed and afraid all the time.
When James moved to stun him, part of him wanted to jump in front of the spell and take the hit for Sirius. He was so protective of him, that even in an instance like this he wanted to shield him from harm. The only reason he didn't was because he felt that what was happening to Sirius now was a greater danger than a stunning spell.
After it happened, he hurried to join James, knowing they only had a limited amount of time to accomplish this task. He draped the cloak over Sirius, then looked up at James. "We've got to get him somewhere he'll feel safe when he wakes up. Otherwise he's going to completely panic."