I suspect it was the Godfather movies that started the trend of numbering sequels, possibly because it seemed classier.
And if I recall correctly, Coppola had to fight hard with the studio to get the film titled "The Godfather, Part II" because it was virtually unheard of to do something like that, but he felt that the movie was more than just a sequel, it was a direct continuation of the story in The Godfather. Ironically, Coppola didn't want to name the third film The Godfather, Part III, because he didn't feel like it was a direct continuation of the story from the first two films, but rather a related epilogue. He wanted to call it The Death of Michael Corleone, but the studio made him call it Part III, because numbering films had become such common practice by then.