The story I'm looking for was about a guy who cloned himself near the end of his life. The original went to retire (and die) on a space station unable to contact anyone outside the station. The clone ended up living ages and watched society evolve. The clone may have also dated the clone of his crush?
It tackled the ethics of copying consciousness and was the first Sci-fi story I read that actually made me love Sci-fi. I would love to find it, but infuriatingly I can't remember much else. I know it was in a best of short stories fiction book, and I can't remember any other stories in the book. I don't think it was Years Best SF.
I will update this post if I find/remember anything else.