Jean Pierre Blanchard launched the first hot-air balloon flown in the United States of America from Walnut Street, Philadelphia, in early 1793. The flying balloon and soaring aeronaut stunned and captivated the citizens of Philadelphia. A subsequent planned balloon flight was rendered impossible by the epidemic described in the novel. Blanchard's yellow silk balloon is presented as a symbol of hope in the novel, and Mattie compares it to the rising sun that starts a new day.
And of course, fever, or malaria, was often called Yellow Fever because it turned eyes yellow.
Are you sure it symbolyzes hope? I think the balloon itself represents Mattie and the ropes mother.