When Peter took part of the blame, how did Aslan respond? Why do you think he responded this way?

Aslan didn't respond to Peter.... he merely left it at it was. We can infer that Aslan didn't want to place blame, he was content with the fact that Peter had been mature enough to accept part of that blame. There was nothing left to say.

And Aslan said nothing either to excuse Peter or to blame him but merely stood looking at him with his great unchanging eyes. And it seemed to all of them that there was nothing to be said.