Middle English rein, from Old English regn "rain, descent of water in drops through the atmosphere," from Proto-Germanic *regna- (source also of Old Saxon regan, Old Frisian rein, Middle Dutch reghen, Dutch regen, German regen, Old Norse regn, Gothic rign "rain"), with no certain cognates outside Germanic, unless it is from a presumed PIE *reg- "moist, wet," which may be the source of Latin rigare "to wet, moisten" (see irrigate).
Rain dance "dance performed by a tribal group in hope of summoning rain" is from 1867; rain date in listings for outdoor events, giving an alternative date should rain interrupt them on the intended day, is from 1948. To know enough to come in out of the rain (usually with a negative) "take ordinary measures for one's protection" is from 1590s. Rain-shower is Old English renscur. Rain-gauge "instrument for collecting and measuring the amount of rainfall at a given place" is by 1769.
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/rainy">Etymology of rainy by etymonline</a>
Harper, D. (n.d.). Etymology of rainy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/rainy