inch

Inch comes from Middle English ynche, from Old English ynċe, which was borrowed from Latin ū̆ncia, meaning a Roman inch or similar small unit, ultimately tracing back to the Proto-Indo-European word for "one."

The facts given don't show a documented shift in meaning — the word has denoted a small unit since its Old English borrowing from Latin.

Inch is a doublet of ounce — both descend from the same Latin word ū̆ncia, just borrowed into English at different times and settling into different meanings.