[Seeing Xion's little note left behind left Axel feeling bad and good at the same time. For one thing he actually appreciated that she was getting the hang of letting them know when and where she'd be going somewhere. Unfortunately seeing her handwriting and the name "Suzaku" printed on it brought a mix of displeasing feelings. It's understandable why he would react that way toward seeing Suzaku's name, but her handwriting, well, that's a different story.
It belongs to Xion, it's a part of her, but Xion as a whole...isn't exactly real. The memories he scanned earlier that day contained vital information about the replica project and what the Organization had been planning to do with her. They hadn't planned on her birth and they hadn't planned on even using her, but Xemnas knew something Axel didn't and something tells him that Xion lost in the end. He doesn't yet know how, and maybe he never will, but that's why he has that second disc to help him out.
He'd been contemplating watching it until he realized that the sun had gone down and Xion still wasn't home. So, figuring that she'd be somewhere around the neighborhood, Axel heads out with Pluto to start looking. The puppy follows at his side and starts sniffing about either for a place to do his business or for where Xion might be; Axel doesn't know.]