I’ve used these words (きる・つく) in conversations for decades, having no idea they used the same kanji.
After finding no less than thirteen definitions for 着くin the dictionary (#13: “to be lucky”!) I’m starting to think someone is pulling my leg.
I asked my (Japanese) wife about it, and to my surprise she didn’t feel the wear/arrive meanings seemed unrelated at all. She said 着く can be used with clothing, too. She then mimed vague “putting on a shawl” motions while looking at me like that should explain it.
Despite her best efforts, I remain mystified.
I’m all too familiar with Japanese inscrutability, but I was curious if anyone here more fluent in both languages might be able to explain how this particular character can have these two utterly dissimilar meanings (or how Japanese people could possibly consider them similar!).
I know this kind of weirdness abounds, but these words are so common it fascinates me.