Think of how different the doctors reaction is between Amy's Choice, and Angels Take Manhattan. In Amy's Choice when Amy decides to kill herself to follow Rory, The Doctor tried to convince her not to, but then decides to go along with it. He knows that if it wasn't the dream he could just regenerate, but he would loose Amy forever. And just like when Martha left by her own choice, he lets her go. The Doctor never forces anyone to stay, he wouldnt beg anyone to continue to travel with him against their will. But when Amy decides to go after Rory when the weeping angel gets him... He begs her not to go, he cries and pleas with her... He never did that with any other companion... He falls to the ground and begs her not to go... And Amy; she knew The Doctor her whole life... That was all she knew, traveling with him. She left her daughter with the doctor, she left her whole life to be with Rory. I would argue that Amy loved Rory just as much as Rory loved Amy. 2000 years is a long time, but Amy has proved her love in equal amounts. What gets me is how, to The Doctor, Amy and Rory have been the most important companions. He goes back to visit them before they leave, just to see them again. He begs them not to jump, and he has risked his own existence to save them. They brought him another timelord. They are more than just companions that he is showing the universe to; he shared 100 of his years with them... They are the only family he had... And he can never see them again