How does the mood of The Metamorphosis by Franz Kafka contribute to the story?

The mood in "The Metamorphosis" is tense (or intense) from the beginning. Gregor wakes up as the insect and the subsequent events, such as dealing with a clerk from his office and being discovered by his family are traumatic, tense situations. The entire period from the time he wakes up until Grete's violin solo and his death is one long battle to adjust to his new body and try and relate to his family, which seemed to be a problem even prior to his metamorphosis. The intensity is interrupted only once in a while. For example, there is a moment when Gregor gets control of his legs and feels a sense of physical comfort.

The mood is also gloomy and constricting. It continues to rain outside and since Gregor is confined to his room, the mood isn't just gloomy and intense; it's also claustrophobic. Being stuck in his room, Gregor is a prisoner. This is a direct parallel to his former life when he was forced to work a job he hated to provide for a family that did not appreciate him. 

It isn't until Gregor dies that the mood (and setting) changes. Gregor's mother, father and sister leave the apartment: 

Then all three left the apartment together, something they had not done for months now, and took the electric tram into the open air outside the city. The car in which they were sitting by themselves was totally engulfed by the warm sun.

How does Kafka's characterization in The Metamorphosis influence the reader's perception?

In The Metamorphosis, Franz Kafka tells the story of Gregor Samsa, who has been transformed into a "monstrous vermin" (commonly inferred to be a cockroach).

Kafka's characterization of Gregor influences the responder's reception of him by making him extremely sympathetic. Gregor seems to have been an average man with a lot of love for his family, and yet when the transformation occurs, he is slowly but surely neglected by the very family whom he had spent his human life caring for. Although they at first make efforts to accommodate him, in particular his mother and sister, they eventually start to view his existence as a burden upon them.

They begin to place their needs above his, and his father even physically hurts him twice—once while trying to push Gregor back into his room, and once by hurling apples at him to chase him away from the family's main living space. Even when Gregor dies, the family reacts with relief instead of mourning him. Gregor, meanwhile, seems to harbor no ill-will about his treatment, reacting with hurt, but not resentment.

In this way, Kafka elicits a lot of sympathy from the responder for Gregor's overall plight.