[This, to him, seems like the best way to show someone that they're wanted. He likes kissing, but he doesn't know how to convey the kind of affection that he'd like to show Kitty that way. Kissing someone, in his mind, demonstrates passion; holding them demonstrates love. Kitty might need to give him lessons on more subtle forms of nonverbal communication.
Even though she doesn't seem thrilled about his move, he trusts that she'll do something if she doesn't like it. It doesn't occur to him that something as simple (to him) as who is holding whom could be so meaningful. As she relaxes, he strokes her back in the way that he finds particularly comforting.
Not that she needs to be comforted, not really, but it's what he wants to do. He wants to take care of her. There is so much in life that he can't do much about, from the destruction of the Enterprise to Krall's attempt at wiping out a major Federation base. He does his part, of course, but he's not a hero like Captain Kirk. There's always a feeling of helplessness in the face of a major catastrophe because there's so little that he can do on his own.
Here, with Kitty, maybe he can do something. He can't be the hero (that's her job), but he feels like there is something he can do for her.]