In Late Middle English, “inveterate” referred to long-standing or chronic disease, but that usage has dropped out and changed in the centuries since. It now describes an entrenched habit or interest — for example, an inveterate practice of two cups of coffee every morning while reading the paper. The adjective originates from the Latin “inveteratus” (“made old”), and you would be correct if you recognized a shared root with the word “veteran.” The latter noun is defined as “a person who has had long experience in a particular field,” and that sort of experience often leads to inveterate habits.