The analyses of a text #3

The narrator recalls his adolescence.
He visited his old nurse Peggoty's several years after the first visit, who lives in his home town with her husband, a coach man, Mr. Barkis
And he met Mr. Barkis who was laid up in bed with acute rheumatism.
And then the narrator's best friend Steerforth visited Peggoty's because of his promising to do so, and they had a good time.

..............................
When Peggotty spoke of what she called my room, and of its being ready for me at night, and of her hoping I would occupy it, before I could so much as look at Steerforth, hesitating, he was possessed of the whole case.
"Of course," he said. "You'll be sleep here, while we stay, and I shall sleep at the hotel."
"But to bring you so far," I returned, "and to separate, seems bad companionship, Steerforth."
"Why, in the name of Heaven, where do you naturally belong!" he said. "What is 'seems,' compared to that" It was settled at once.
[David Copperfield by Charles Dickens]
1. I'd like to know what "was possessed of" means here.
2. And I'd like to know what "that" refers to.
Thank you in advance for your help.