Why not just ask him? "Hey, I notice that your stutter seems to really get you down sometimes. Do you want to talk about it? Is there anything I can do to be helpful?" You could also find something positive or helpful about the stuttering community and bring it up. Like have you ever listened to Stutter Talk? It's a podcast all about stuttering news and research. The B Team is my favorite. You could ask him if he has heard of it, or if he wants to listen to it. There are plenty of other things, including movies and books, about stuttering that you could bring up that could start a conversation.