There is no clear reason, apparently, but...
For many years in the Middle Ages, people believed that when you sneezed, your spirit left your body for a second. So, the thought went, to say "bless you" could bring you back to life and also keep evil spirits from entering you in the instant or two that you were believed to have been gone.
During the bubonic plague saying "God bless you" offered a desperate prayer for health and protection against the deadly disease. Pope Gregory is said to have encouraged people to embrace these blessings during that doom-filled era.