You can read about this in Chapter 16. Heathcliff is out in the garden outside Catherine's window while she is giving birth to young Catherine. Catherine dies two hours later. Heathcliff's mourning for her is as passionate as his love for her was when she was alive. He curses Catherine for causing him such pain in his life but then pleads with her spirit to haunt him for the rest of his life. He says he does not care what form she takes, she can even drive him to madness, as long as she never leaves him. Weird, huh?
Heathcliff stays out in the garden all night. When Edgar leaves Catherine's side, Nelly lets him in for a brief moment and he takes a piece of his hair and puts it in Catherine's locket instead of Edgar's hair. When he leaves, Nelly takes both locks of hair and winds them together, then closes the locket. This is symbolic of the two men in Catherine's life - Heathcliff and Edgar - the two men that loved her. Heathcliff goes from bad to worse after Catherine's death.
I believe Heathcliff's grief frees him to show his true character. Not only is he this gruff guy, but he truly experiences the feelings of love for Catherine. His overt lack of self-control explicitly shows these feelings. I love that he doesn't hold back. And doesn't care what others think!