Why the Waif?

Why was the specter or ghost Lockwood saw outside the window a child? When I was the reading the beginning of the book, I thought that malybe Catherine was only a childhood friend of Heathcliff's and so, he remembers her as only a child. However, we find out that much more than that happens (since they both grow into adults before Catherine dies). So why is the ghost a child instead of a woman? Also, I don't understand why Heathcliff was so desperate to make the specter return because towards the end of the book, some time before Heathcliff dies, he mentions that he has been haunted by Catherine's ghost for years and years. So why was he so moved by the specter in the window if he sees them everyday?