1764, intransitive, "indulge in sentiments," from sentimental + -ize. Meaning "to make sentimental" (transitive) is from 1813. Related: Sentimentalized; sentimentalizing.
Think on these things, and let S______ go to Lincoln sessions by himself, and talk classically with country justices. In the meantime we will philosophize and sentimentalize;--the last word is a bright invention of the moment in which it was written, for yours or Dr. Johnson's service .... [Laurence Sterne, letter to William Combe, Esq., dated Aug. 5, 1764, published 1787]