Soukyuu no Ariadne

Lacile lives in the mountains with his grandfather and two younger siblings, always gazing at the sky and dreaming of the legendary Flying City of the Heavens. One day, he meets Laana, a strange young woman who can glide through the air unless she wears heavy steel boots to hold her down. Laana also dreams of seeing the outside world, even if only once before she is offered in marriage. When machine warriors pursue her, Lacile discovers that she is the princess of the Ariadne Empire, a home that floats in the sky.