late 14c., plage, "affliction, calamity, evil, scourge;" early 15c., "malignant disease," from Old French plage (14c.), from Late Latin plaga, used in Vulgate for "pestilence," from Latin plaga "stroke, wound," probably from root of plangere "to strike, lament (by beating the breast)," from or cognate with Greek (Doric) plaga "blow," from PIE root *plak- (2) "to strike."
The Latin word also is the source of Old Irish plag (genitive plaige) "plague, pestilence," German Plage, Dutch plaage. Meaning "epidemic that causes many deaths" is from 1540s; specifically in reference to bubonic plague from c. 1600. Modern spelling follows French, which had plague from 15c. Weakened sense of "anything annoying" is from c. 1600.