1640s, "downy, fuzzy," later "flimsy, unsubstantial" (1660s), of unknown origin; one theory is that it is a corruption of Silesia, the German region, where thin linen or cotton fabric was made for export. Silesia in reference to cloth is attested in English from 1670s; and sleazy as an abbreviated form is attested from 1670), but OED is against this. Sense of "sordid" is from 1941. Related: Sleazily; sleaziness.
A day is a more magnificent cloth than any muslin, the mechanism that makes it is infinitely cunninger, and you shall not conceal the sleazy, fraudulent, rotten hours you have slipped into the piece, nor fear that any honest thread, or straighter steel, or more inflexible shaft, will not testify in the web. [Emerson, "The Conduct of Life," 1860]