The verb 'stay' entered Middle English from the Old French 'estayer' or 'estaier', meaning 'to prop up or support'. This French term likely derived from a Frankish or other Germanic source related to the concept of standing firm, akin to the Old High German 'stān' (to stand). The core semantic journey is from the physical act of propping something up, preventing it from falling, to the more abstract sense of remaining in a fixed state or position. The noun senses, such as a supporting brace or a period of residence, developed naturally from this foundational idea of providing stability or causing something to remain.

The word 'stay' is a simplex word of Old French origin. It is not productively composed of smaller, separable morphemes in modern English.