1580s, "worthy of notice or observation" (a sense now obsolete); 1590s, "worthy of esteem by reason of inherent qualities;" see respect (v.) + -able.
Of persons, "having an honest reputation" from 1755; the sense of "moderately well-to-do and deserving respect for morality; occupying a fairly good position in society" is by 1800. From 1755 as "considerable in size or number;" from 1775 as "not too big, tolerable, fair, mediocre." Related: Respectably.
word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).
Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]
Others are reading
<a href="https://www.etymonline.com/word/respectability">Etymology of respectability by etymonline</a>
Harper, D. (n.d.). Etymology of respectability. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/respectability