Middle English prechen, "deliver a sermon, proclaim the Gospel," from late Old English predician, a loan word from Church Latin; reborrowed 12c. as preachen, from Old French preechier "to preach, give a sermon" (11c., Modern French précher), from Late Latin praedicare "to proclaim publicly, announce" (in Medieval Latin "to preach," source also of Spanish predicar), from Latin prae "before" (from PIE root *per- (1) "forward," hence "in front of, before") + dicare "to proclaim, to say" (from PIE root *deik- "to show," also "pronounce solemnly," and see diction). Related: Preached; preaching.
Meaning "give earnest advice, especially on moral subjects" is by 1520s. To preach to the converted is recorded from 1867 (the form preach to the choir attested from 1979).
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
<a href="https://www.etymonline.com/word/preachy">Etymology of preachy by etymonline</a>
Harper, D. (n.d.). Etymology of preachy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/preachy