The Angels Take Manhattan is about endings. Not the end of the world, or the universe, or time, like past epic stories have been about. It is about regular human endings, about saying goodbye and the things in life that keep us from the people we love. It is about leaving Neverland, finding that Peter won't be coming back for you after all, even though he might want to.
The theme of endings is played with from the opening on: the Doctor tearing out the last page of his book and declaring "I hate endings" is paid off at the end of the story with Amy's line "You and me, on the last page". The dialogue throughout the episode is poignant, but this pair of lines perfectly bookends it. Rory's death is also (once again) hinted at throughout the episode. And as a counterpoint to the theme of endings, we have references to the last two and a half years scattered throughout this episode - small moments or lines of dialogue that echo Amy and Rory's story. That this is a departure story is coded deeply and obviously into this episode.
So, what force could possibly pull Wendy from Neverland? The answer is, of course, right there in the title: the Weeping Angels.
When I first watched Blink, it seemed to me that while they were a very clever idea, the Angels could only really work once, because there was only one story they were really suited for, and I had just watched it. So, I went in to The Time of Angels warily. And it turns out there was something else you could do with the Angels - collide them into a space marine action film and then suddenly change that into a story about trust. The Time of Angels also made the angels much scarier by suggesting that they were born in imagination, by thinking about them.
And coupled with this is a realization that didn't hit me until the second time I watched Blink: the Angels can move when nobody is looking at them. Yet repeatedly, in stories with the Angels, they are clearly visible as still statues when *none of the characters* are looking at them. Diegetically, then, they should be free to move, to zap their prey back in time.
So why do they stay stone-faced? The most interesting answer - and it seems consistent with Moffat's thematic tendencies and understanding of the franchise - is that the Angels have an meta-diegetic existence. They have to remain stone because *the viewer* is watching. Time of Angels also established, of course, that the Angels defense mechanism is based in part on their perceptions; they will remain stone as long as they *think* you can see them.
In other words, the Angels know you are watching them. They can see you.
And just in case you feel safe with the knowledge that it's only a television show, remember that even diegetically, they were born from imagination. They are by their nature written into existence.
But in The Angels Take Manhattan, it isn't just the Angels that have a hinted-at meta-diegetic existence. The entire episode plays heavily according to narrative logic, so much that it acquires the existence of the viewer in order to make basic sense. The first instance of this is when the Doctor explains that reading ahead - knowing your own personal future - makes it inevitable. That you can still change things as long as you don't know they are going to happen. Immediately after this declaration, though, Rory's name is shown on a tombstone. Note that this event is now inevitable - a fixed point has been created, to borrow the Doctor's phrase. But none of the *characters* have seen the tombstone, only the audience. And yet the fact that our seeing the tombstone makes Rory's death inevitable is clearly the intent of the narrative - otherwise there is no reason for it to be juxtaposed with the Doctor's speech about spoilers.
The other example is the Doctor's statement that they are allowed to read "things that are happening now, in parallel". There are two ways to read this: 'parallel' can mean 'written events that correspond with what we are doing right now'. But it also suggests that the two sets of events, in different time periods, are somehow happening at the same intrinsic 'moment'. Russel T Davies hinted at this idea in The End of Time, as well, when Rassilon says that the Doctor is "in possession of the Moment". But the 'present moment' in a story is really the moment that is receiving Narrative Focus. The "present" is the part of the story we're reading. This applies equally well to River's book and to the episode of Doctor Who.
So the diegetic rules of the narrative universe can operate on the meta-narrative level. This isn't really anything new for Doctor Who, but it has never been used this extensively before.
So the Angels have some amount of awareness of the narrative, and this gives them the power to attack the narrative. They never threaten to destroy the show completely, but they are able to write Amy and Rory out of it. And yet they exit with a dignity that few companions have ever been afforded. They die, but in a very normal, human way, after a full and normal life. They are ripped from Neverland, and that is tragic, but they still find a way to be happy.
And so Rory grows up, and adopts a son, who will eventually track down his grandfather and deliver a letter to him at a particular time and place. From his perspective, his son and daughter-in-law have barely been gone any time at all. This is a powerful parallel to the first appearance of the Angels, and a wonderful final note for Rory. It is a shame it didn't make it into the episode. I agree with the decision to cut it, though - the final notes for the episode are on Amy and the Doctor, which is correct. Rory receives the focus of the narrative for most of the episode itself, and Amy's departure hinges on her choice of Rory over the Doctor. Thematically, Brian's scene would have weakened the ending. It is better where it is, as a piece of para-textual lore, present but not interrupting the main narrative.
And so Amy grows up, not resenting a Doctor who never came back for her, but missing a friend who was separated by circumstance. It is a much kinder ending than I expected. And it comes on the heels of a story that emphasizes that leaving Fairyland is not a necessity, that it is okay to run away and stay a Fairy Child forever. So we know that this separation is cruel and unnecessary, required diegetically only by circumstance and meta-diegetically by the format of the show (which requires that companions come and go). The show has explicitly avoided allowing a reading that says we have to eventually grow up. Sometimes we do, but not because it is the only path to happiness.