I have a stutter— so does a new friend I have made

I have a stutter— so does a new friend I have made I’ve always stumbled on my words in stressful, emotional, happy, or exciting situations (very very badly when I’m tipsy). It’s noticeable but does not happen that often at all, and only my close friends and family really notice it. I have made a friend recently who stutters in 99% of his sentences. We have great conversations and I like talking to him. However, my stutter amplifies to almost every sentence whenever speaking to him. It is never this bad. I do stutter when talking to him but my words are more easier to get out than his, he has a lot more difficulty with it. I worry that he thinks I am stuttering to make him feel better or something. My biggest concern would be him think I’m mocking him. Is there something I should say to him about it so he knows I’m not just mocking him? I’m sure he sees me talking to other people and not stuttering nearly as bad as I do with him and it makes me feel crappy. Does anyone else with a stutter notice “mirroring” with some people? How does this make you feel?