Old English þræd "fine cord, especially when twisted" (related to þrawan "to twist"), from Proto-Germanic *thredu- "twisted yarn" (source also of Old Saxon thrad, Old Frisian thred, Middle Dutch draet, Dutch draad, Old High German drat, German Draht, Old Norse þraðr), literally "twisted," from suffixed form of PIE root *tere- (1) "to rub, turn." Meaning "spiral ridge of a screw" is from 1670s. Threads, slang for "clothes" is 1926, American English.
The silk line, as spun by the worm, is about the 5000th part of an inch thick; but a spider's line is perhaps six times finer, or only the 30,000th part of an inch in diameter, insomuch, that a single pound of this attenuated substance might be sufficient to encompass our globe. [John Leslie, "Elements of Natural Philosophy," Edinburgh, 1823]