Melancholy and hopelessness
This novel is a bit of a Gothic tale, and its tone reflects that. All the kids in the Grape family are devastated by the suicide of their father, and so the seven children represent various aspects of melancholy and depression. Gilbert feels trapped, Amy feels nostalgic for when they all used to be happy, Ellen feels angry and resentful, Janice escaped, Larry has serious mental health issues from finding their father dead, Arnie often becomes agonized when he remembers the death of his father, and there a seventh child who stays away from the family completely. The novel is at least in part a picture of grief, pain, and depression, but of course it also has hope and romance and joy, all mixed in with the pain.
Tragedy, death, and horror
Besides the emotional lives of the children, the trauma of their father's death had another toll. It had tragic effects on the mother, leaving the family broken and unbalanced. Also, Arnie's health is precarious, and he is always finding ways to threaten his safety, just because he doesn't know better, and he likes the attention. So, Gilbert is always paranoid about Arnie's death. Death is on the table for another reason too. Gilbert's mom is so obese that she might literally die any day, for two reasons, heart attack, or falling through the floor and dying in the basement where her husband killed himself. In the end, Gilbert's mom faces death with honor by climbing to their bedroom upstairs to lay down for her final rest. She dies in her own bed, which she had not done ever since the incident. The other option was sink in through the floor and die that way, so thematically, this is a picture of honor and victory in death.
Family, love, and honor
Honor itself is a major theme in the novel, both for the scene just mentioned above, and for a long list of others. Gilbert does something dishonorable with a married woman, and it haunts him. Becky is too young for Gilbert to do anything with, so he is constant attempting to be honorable in their friendship. He has a sacred oath to protect Arnie in any circumstance, but he loses his temper and hits Arnie in the head while yelling at him. That is his major failure in the novel, of course, and it leaves him without any honor. He feels perfectly ashamed, and because of that shame, he stays away (like his other siblings have stayed away), but when he returns (like his other siblings do), he is accepted back into the fold. It seems family love is greater than his shame. His honor comes from his willingness to serve his family, and when they burn the house to the ground, they do it to honor their mother's legacy.