Sometimes certain burial/mourning traditions go along with the type of animal. For example, there are often specific responses to the death of a race horse, and that is in part because of the animal's size -- for example, a tradition with race horses is to only bury their head, hooves, and heart and cremate the rest. But in terms of the grief people feel in response to their animal's death, it doesn't matter if it is a bird or a dog or a horse -- it all depends on that person's relationship with the animal. Some people who maybe, say, have a cat and a hamster might feel more sadness over the cat's death because they had the animal longer, but that isn't always the case. People I spoke with who had tarantulas mourned them just as deeply as people who had dogs. Grief is grief.