Artifacts on wavy lines in Illustrator

I have a wavy line that I originally draw with the brush tool and have edited a bunch with the anchor point tool. When I decrease the thickness of the line the artifacting goes away, but when I increase the thickness the artifacting appears. It isn't that visible but it frustrates me and makes the edges of the lines feel rougher than I would like them to. I have tried messing with some of the settings mentioned in other posts, but it may be a different issue than what I'm experiencing.

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