Old English þynne "narrow, lean, scanty, not dense; fluid, tenuous; weak, poor," from Proto-Germanic *thunni "thin" (source also of West Frisian ten, Middle Low German dunne, Middle Dutch dunne, Dutch dun, Old High German dunni, German dünn, Old Norse þunnr, Swedish tunn, Danish tynd), from PIE *tnu- "stretched, stretched out" (hence "thin"), from root *ten- "to stretch" (source also of Latin tenuis "thin, slender").
These our actors ... were all Spirits, and Are melted into Ayre, into thin Ayre. [Shakespeare, "The Tempest," IV.i.150, 1610]
"Loose or sparse," hence "easily seen through," with figurative extensions. Related: Thinly; thinness. Thin-skinned is attested from 1590s; the figurative sense of "touchy" is from 1670s.