mid-13c., "story of a building;" early 14c., "raised platform used for public display" (also "the platform beneath the gallows"), from Old French estage "building, dwelling place; stage for performance; phase, stage, rest in a journey" (12c., Modern French étage "story of a house, stage, floor, loft"), from Vulgar Latin *staticum "a place for standing," from Latin statum, past participle of stare "to stand," from PIE root *sta- "to stand, make or be firm." Meaning "platform for presentation of a play" is attested from late 14c.; generalized for "profession of an actor" from 1580s.
Sense of "period of development or time in life" first recorded early 14c., probably from Middle English sense of "degree or step on the 'ladder' of virtue, 'wheel' of fortune, etc.," in parable illustrations and morality plays. Meaning "a step in sequence, a stage of a journey" is late 14c. Meaning "level of water in a river, etc." is from 1814, American English.
Stage-name is from 1727. Stage-mother (n.) in the overbearing mother-of-an-actress sense is from 1915. Stage-door is from 1761, hence Stage-Door Johnny "young man who frequents stage doors seeking the company of actresses, chorus girls, etc." (1907). Stage whisper, such as used by an actor on stage to be heard by the audience, first attested 1865. Stage-manage (v.) is from 1871.