Johanna Weber was born in Düsseldorf, Germany. In 1929 she began her studies in chemistry, mathematics, and physics at the University of Cologne (Universität zu Köln) before switching to Göttingen University. She graduated with first-class honors in 1935, then studied for two years to become a teacher. After being refused a teaching post since she was not a member of the Nazi Party, she began working in industry, eventually becoming a world leader in the field of aerodynamics during her career in Germany and later England.
An extensive biography of Johanna Weber by John Green can be found in the obituary he wrote for the Royal Aeronautical Society. Other obituaries are given in the references below.