Be patient when he stutters. I hate when people try to finish my words or sentences. Just be patient. I would definitely talk to him about it in private, but don’t badger him if he doesn’t want to talk about it. Just make him feel safe and let him know that IF he wants to talk about it, you’re there for him. It may have something to do with his self esteem, or maybe not. I’ve been stuttering since the age of four. So I know that my stutter probably didn’t come about because of self esteem, but I definitely see a difference in my stutter when I’m not feeling good about myself. Stuttering fluctuates for many, and I’m sure your brother would be happy to know that you’re there for him, with no judgements. Hope this helped! :)