Yours, Etc.: Origins and Uses of 8 Sign-Offs
Old English stearc "stiff, strong" (related to starian "to stare"), from Proto-Germanic *starkaz (cf. Old Norse sterkr, Old Frisian sterk, Middle Dutch starc, Old High German starah, German stark, Gothic *starks), from PIE root *ster- "stiff, rigid" (see stare).
Meaning "utter, sheer, complete" first recorded c.1400, perhaps from influence of common phrase stark dead (late 14c.), with stark mistaken as an intensive adjective. Sense of "bare, barren" is from 1833. Stark naked (1520s) is from Middle English start naked (early 13c.), from Old English steort "tail, rump." Hence British slang starkers "naked" (1923).