In writing fiction, I find myself using the word "absentmindedly" a lot, but I don't think it's really the word I'm looking for. I'm not looking so much something done in a distracted manner, but something done sort of half-consciously, without really thinking about it. Not habitual either, but perhaps almost instinctual.
As James watched the other girl climb higher, he shuddered to think of his own sister being in such danger, and put his arm absentmindedly around her.
What I'm trying to relate is that he wasn't making a conscious move to comfort or embrace his sister, he just did it without thinking.