How did Edgar mourn in Wuthering Heights when Catherine died?

In the novel 'Wuthering Heights' by Emily Brontë, Edgar Linton doesn't mourn at all when Catherine Earnshaw (the love of his life) dies during childbirth when her daughter Cathy was born. On the contrary, Edgar seems quite relieved after Catherine’s death. He believes this event as God’s punishment to Catherine for rejecting Linton and marrying Heathcliff. Instead of grieving, Edgar shows more love and concern towards Catherine’s and Heathcliff’s daughter, who is given the same name - Cathy after her deceased mother.