[. . .Why does it feel like he needs to be doing something here? Like he's put on the spot and needs to step up his trust game.]

I suppose he could see you genuinely care for him, working hard to keep him together. I'm certain he's been on his own for a long time, much longer than me. [He gets it, being able see someone they can rely on for once. He tilts his head, considering her words a little more.] Are you worried you can't be relied on?