c. 1300, "proud, valiant, strong," from Old French estout "brave, fierce, proud," earlier estolt "strong," from a Germanic source from West Germanic *stult- "proud, stately, strutting" (source also of Middle Low German stolt "stately, proud," German stolz "proud, haughty, arrogant, stately"), from PIE root *stel- "to put, stand, put in order," with derivatives referring to a standing object or place.
Meaning "strong in body, powerfully built" is attested from late 14c., but has been displaced by the (often euphemistic) meaning "thick-bodied, fat and large, bulky in figure," which is first recorded 1804. Original sense preserved in figurative phrase stout-hearted (1550s). Related: Stoutly; stoutness.
1670s, "strong beer or ale," from stout (adj.). Later especially, and now usually, "porter of extra strength" (by 1762).