sneeze v.

late 15c., snesen, from or replacing fnesen, which is Old English fneosan "to snort, sneeze," from Proto-Germanic *fneusanan. Compare: Middle Dutch fniesen, Dutch fniezen "to sneeze;" Old Norse fnysa "to snort;" Old Norse hnjosa, Swedish nysa "to sneeze;" Old High German niosan, German niesen "to sneeze," all from Proto-Germanic base *fneu-s- "sneeze," which is of imitative origin, as is PIE *pneu- "to breathe" (source of Greek pnein "to breathe").

Other imitative words for it, perhaps in various ways shaped by one another, include Latin sternuere (source of Italian starnutare, French éternuer, Spanish estornudar), Breton strevia, Sanskrit ksu-, Lithuanian čiaudėti, Polish kichać, Russian čichat'.

The Middle English shift to sn- might be due to a misreading of the uncommon digraph fn- (represented in only eight words in the Clark Hall dictionary, mostly words having to do with breathing), or from Norse influence. But OED suggests it wasn't a direct evolution, and that Middle English fnese had been reduced to simple nese by early 15c., and sneeze is a "strengthened form" of this, "assisted by its phonetic appropriateness." Related: Sneezed; sneezer; sneezing.

To sneeze at "show contempt for, regard as of little value" (usually with negative) is attested from 1806. To teach (one) how the cat sneezes apparently was an old phrase for "to dominate, bully."

Off þat ʒong gentil man was a gret disese

After a ʒere or two his wyfe he myʒt not pleese

... Sche tauʒt hym euer among how the katte did snese.

[from "Tale of the Basin," c. 1500]

"act of sneezing, sound made by sneezing," 1640s, from sneeze (v.).