"a bending or drooping," 1580s, in nautical use, "movement to leeward," from sag (v.). From 1727 in American English in reference to landforms having a sunken look. By 1861 in reference to droop from slackness in wires, cables, etc.
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/saggy">Etymology of saggy by etymonline</a>
Harper, D. (n.d.). Etymology of saggy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/saggy