Manga Soukyuu no Ariadne

Living in the mountains with his grandpa and his two little sisters, Lacile has always looked to the sky. He has dreams of seeing the fabled Flying City of the Heavens — and one day his dream just might come true. One day, he crosses paths with a strange girl named Leana who has the peculiar ability to float away unless she wears heavy steel boots that keep her on the ground. Like Lacile, Leana has dreams — she wanted to see the outside world just once before she’s married off. But when machine soldiers pursue her, Lacile learns the truth: Leana is actually the princess of the Ariadne Empire, and her home floats in the sky…