It wasn't a sudden change, it's been a gradual tendency towards them. James Bond was already 19 films by the turn of the century (or 20 if you include the other Casino Royale), King Kong and Star Trek both got to 6, Batman 8, Star Wars had just had the 4th, Friday the 13th had reached 9 films.

Even BttF itself was three films, and in the second one was parodying the tendency towards sequels with the holographic Jaws 19.