This Doctor, Twelve, he’s lived billions of years without River. He said goodbye to her for one final time (or so he thought) in his previous incarnation. It’s been YEARS since he last saw her.
Then suddenly she is back, just before Darillium. For someone to have spent so many years away from someone, it is easy to forget them but the Doctor kept her in his thought, in his mind. He saw her, he smiled, he laughed, he held her hand.
He reassured her he loves her in the most beautiful way. He stood by her, fought with her, he stayed back. For someone who’s been away from someone they care about for almost a billion years, he stayed back with her, so that he could make sure her diary ended with the happiest memories.
River is a part of his life he just can never give up. He doesn’t know hot to say ‘I love You’ but he shows her in the most amazing way, by giving her ‘Time’ for someone who’s running through all of space and time, he gave her time with him.
I don’t know if someone can love someone more than this. I don’t know if its possible. Billions of years apart yet the love stayed the same.
That’s why the episode ended with “and they lived happily…” Because stories like this don’t end, they go one for an eternity and beyond.