Well if you know anything about that, LOTR is not really three separate stories. It is all one. Tolkien designed it as one book, but publishers forced him to separate it into three books. So the story is one.
It is not a weak movie. Movies don't have to stand alone to be "good". It does not hurt, but some films have such vast narratives such as LOTR one film won't cut it. With LOTR the extended cuts together are around 11 and a half hours long.
The books were never designed to be stand alone books. But they were forced to be so. And again......the films are praised as well as the books for a reason. Just like Godfather Part 1 and 2, as well as some one said about the Star Wars OT.
EDIT: As for the sequel thing. TDK is a sequel as much as anything else. The story can stand alone, but the themes and character arcs are a huge part of it. And if you only see TDK most will not understand the full depth of the journey of this character. And the third will be no different. It is a continuation of characters previously built. The movie can stand alone, but you do miss a huge chunk of character arcs and themes.