"completing or tending to complete," 1670s, from Late Latin completivus "serving to fill up," from past-participle stem of complere "to fill up" (see complete (adj.)).
1867, in dialect, "to pet, indulge" (a child), from doll (n.). Usually with up. Meaning "to dress (up)" is by 1906, American English. Related: Dolled; dolling.