"apt to sag" [OED], 1848, from sag (n.) + -y (2). Related: Saggily; sagginess. Sagging (adj.) "that sags," present-participle adjective, is attested from 1590s.
Entries linking to saggy
sag n.
"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.
-y 2
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). Adjectives such as hugy, vasty are artificial words that exist for the sake of poetical metrics.