"place where something is discarded," by 1921 (in phrase give (something) the deep six), originally in motorboating slang, perhaps from earlier underworld noun sense of "the grave" (1929), which is perhaps a reference to the usual grave depth of six feet. But the phrase (in common with mark twain) also figured in sailing jargon, of sounding, for a measure of six fathoms:

As the water deepened under her keel the boyish voice rang out from the chains: "By the mark five—and a quarter less six—by the deep six—and a half seven—by the deep eight—and a quarter eight." ["Learning the Road to Sea," in Outing magazine, February 1918]

In general use by 1940s. As a verb from 1953.

Latin, literally "the descent of Avernus (is) easy" ["Aeneid," VI.126], in reference to Avernus, a deep lake near Puteoli and a reputed entrance to the underworld; hence, "it is easy to slip into moral ruin."

by 1884, from French mal du sìecle, "world-weariness, atrophy of the spirit, aristocratic boredom, deep melancholy over the condition of the world," supposedly a characteristic condition of young romantics in Europe in the early 19c. It answers to German Weltschmerz.

Latin, "weariness of life; a deep disgust with life tempting one to suicide."

also hay-fever, 1825, from hay + fever. Also called summer catarrh (1828); not much noted before the 1820s, when it was sometimes derided as a "fashion" in disease.

People are apt to sneeze, in hot weather for example; and people do not die of sneezing now-a-days, as they did in days that no one knows any thing about. We cannot give six draughts a-day, at one and nine pence each, for sneezing: call it the hay-fever. What a wonderful man! what a clever man! he understands the hay-fever: call him in! Thus is the hay-fever among the last in the list of fashionables. ["On Fashions in Physic," London Magazine, October 1825]

late 14c., from sea (n.) + high (adj.) with sense (also found in the Latin cognate) of "deep" (compare Old English heahflod "deep water," also Old Persian baršan "height; depth"). Originally "open sea or ocean," later "ocean area not within the territorial boundary of any nation."

1944, in reference to the Holocaust, probably translating German Todeslager; they also were known as extermination camps (German Vernichtungslager); historians usually count six of them: Auschwitz-Birkenau, Chełmno, Bełżec, Majdanek, Sobibór, Treblinka.

"star of David," six-pointed star, symbol of Judaism or Zionism, 1904, from Hebrew maghen Dawidh "shield of David," king of Judah and Israel, who died c. 973 B.C.E.

"group of experts assembled to give advice on some matter," occasionally used since early 1900s, it became current in 1933, in reference to the intellectuals gathered by the administration of incoming U.S. President Franklin D. Roosevelt as advisers; from brain (n.) + trust (n.).

also gladhand, 1903, from verbal phrase to give the glad hand "extend a welcome" (1895); see glad (adj.). Often used cynically. Related: Glad-handed; glad-handing.