How do I show him that I care?

I've been friends with this guy for over a year now, and he's great. However, he always downgrades himself and it sucks. Him and I never really have serious conversations about how he feels because our friendship is pretty much just banter and teasing each other, but he says things that people hear and know he is not necessarily okay. I ask him what's wrong, but he doesn't say much, he just says he'll be fine. This has happened multiple times.

I've told him that I care, but he kinda just brushes it off. I don't think he's the best with showing those sorts of feelings. He's such a great guy and I really look up to him, and seeing him upset makes me upset. What should I do to show him that I really do care, even if we don't talk about that stuff? He has opened up to me about some stuff, but then he shuts me out about other stuff but I still hear about it from others.