Curious ends in -ous, one of the standard Latin adjective endings in English, and it came in during the mid-1300s from Old French curios and directly from Latin curiosus, "careful, diligent, inquiring eagerly, meddlesome." The root is cura, "care" — the same word behind cure, curate, secure and accurate.
The link between care and curiosity is the whole history of the word. Latin curiosus meant both painstaking and nosy, and English inherited both: the earliest English senses are "subtle, sophisticated" and "wrought with care and art," alongside "eager to know," often disapprovingly. The modern objective sense, meaning something that excites curiosity, is only from 1715. Booksellers later used curious as a euphemism for pornographic, and such material was catalogued as curiosa. Curiouser and curiouser is Lewis Carroll, 1865.
curious (adj.) mid-14c., "subtle, sophisticated;" late 14c., "eager to know, inquisitive, desirous of seeing" (often in a bad sense), also "wrought with or requiring care and art;" from Old French curios "solicitous, anxious, inquisitive; odd, strange" (Modern French curieux ) and directly from Latin curiosus "careful, diligent; inquiring eagerly, meddlesome," akin to cura "care" (see cure (n.)). The objective sense of "exciting curiosity" is by 1715 in English. In booksellers' catalogues, the word was a euphemism for "erotic, pornographic" (1877); such material was called curiosa (1883), the Latin neuter plural of curiosus . Related: Curiously; curiousness . Curiouser and curiouser is from "Alice's Adventures in Wonderland" (1865). Curious is wonderful on a small scale. [Century Dictionary] also from mid-14c.