So some of this has to do with semantics since it depends on how you're defining sequels and big movies. Even in the earliest days of cinema there were series that would play using recurring characters or sequential adaptations of sources such as plays and pieces of folklore even if they were very loose. There was a popular series of Sherlock Holmes adaptations dating back to 1908 http://m.imdb.com/title/tt0000758/ which continuously started the same actor, Viggo Larsen, as Holmes.
That said, the first "big sequel" in terms of narrative feature films could have been to the first "big movie," namely DW Griffith's Birth of a Nation which is essentially the first feature length film to codify a lot of the techniques and formats seen in narrative films today as well as being a really unfortunate veneration of the Ku Klux Klan. Birth of a Nation was released in 1915 to considerable acclaim and controversy and was followed by The Fall of a Nation in 1916 http://www.imdb.com/title/tt0006664/ . Fall of a Nation was not made by director DW Griffith and was considerably less venerated and is now considered lost, it also does not concern itself with the KKK but with a sort of speculative fiction involving America being taken over by European forces due to American pacifism.
I would have to disagree with the common knowledge that 1916's The Fall of a Nation is the first sequel.
The first sequel to a feature-length film is probably His Majesty, the Scarecrow of Oz, the follow-up to The Patchwork Girl of Oz. Both were released in 1914. Both are long enough to be considered feature films. The first one is 81 minutes, and the second one was originally a little over an hour. And unlike The Fall of a Nation, the cast from the original Oz mostly reprise their roles in the follow-up. Both were produced by the Oz Film Manufacturing Company. And there was a third feature film made at the time as well called The Magic Cloak of Oz, though it wasn't released until 1917.
Another early contender is Tarzan of the Apes and The Romance of Tarzan, both released in 1918, and both starring Elmo Lincoln and Enid Markey as Tarzan and Jane, respectively.
Canine actor Rin-Tin-Tin starred in a series of immensely popular feature films for Warner Brothers beginning in 1923. Also notable are the Dr. Mabuse films, the first of which was made in 1922, but the second not made until 1933, with the same director Fritz Lang and the title role reprised by Rudolf Klein-Rogge.
In the "talkie" era, some of the earliest sequels would be the second films in the feature film series Bulldog Drummond starring Ronald Colman, Charlie Chan starring Warner Olund, Frankenstein starring Boris Karloff, Dracula starring Bela Lugosi, The Thin Man starring William Powell and Myrna Loy, and Sherlock Holmes starring Basil Rathbone and Nigel Bruce.
EDIT: And to answer the second part of the question, His Majesty, the Scarecrow of Oz flopped, just like the first film had, which is why the release of the third film The Magic Cloak of Oz was pushed back to 1917. Though it did get a 1914 release in edited form as a two-reel short subject, which was the more popular form in the early 1910s. It wasn't until the late 1910s or even early 1920s that hour-plus long films became the dominant form used as the main attraction.
So why would Fall of a Nation be considered a sequel then?