The story
- Anglo-Norman · derived fromperuser“use up”
- Medieval Latin · derived fromperūtor
- English todayperuse
From either Medieval Latin perūtor, perūsitō (“wear out”) or Anglo-Norman peruser (“use up”), originally leading to two concurrent meanings, but only those derived from "to examine" survive today. By surface analysis, per- + use.
Etymology from Wiktionary, CC BY-SA 4.0.