1794 "worst condition possible, point of greatest deterioration" (a sense now rare or obsolete), borrowed (by Coleridge) from French pessimisme, formed (on model of French optimisme) from Latin pessimus "worst," perhaps originally "bottom-most," from PIE *ped-samo-, suffixed (superlative) form of *ped- "to walk, stumble, impair," from root *ped- "foot." Compare Latin pessum "downward, to the ground."
As a name given to the metaphysical doctrines of Schopenhauer, Hartmann, etc., that this is the worst possible world, or that everything tends toward evil, it is recorded in English by 1835, from German pessimismus (Schopenhauer, 1819). As "tendency to exaggerate in thought the evils of life or to look only on the dark side," by 1815. The attempt to make a verb of it as pessimize (1862) did not succeed.
"dejected, dispirited," 1580s, creast falne, it has the form of a past-participle adjective, but the verb crestfall is recorded only from 1610s, in reference to diseased horses, and is rare. It's possible that the image behind this use of the word is not having the crest fallen, as a defeated cock does, but horses. Crest-risen "proud, lusty" is from 1610s.