If your patience wears thin, you become less and less patient. This phrase is also used in other contexts, but I have only ever heard it used to refer to "patience". Another meaning is (from Cambridge):
If something such as a joke wears thin, it becomes boring or annoying or stops being funny or effective, because it has been seen, heard, or used too much
I wonder how wear and thin came to be used together and mean that (above).
Dictionary.com dates the first sense (about patience) back to Late 1800s and the other sense to the First half of 1990s but doesn't say anything about how and why they came to be used that way. This Google Ngram shows that "wears thin"/"wearing thin"/"wore thin" has been in use since before 1750.
I am unable to find anything else on the internet.
Can anyone provide some insight?