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Production, drainage and stability of foams films, i.e. films in contact with their menisci, are fascinating problems that remain still unsolved. In this article, we propose to explore the regime of large velocities and large film sizes. This one is not accessible in experiments classically conducted in the literature, and allows us to study the regime of large extension and large extension rates. With our setup, we make soap films up to two meters high by pulling a horizontal fishing line driven by belts out of a soapy solution at velocities ranging from 20~cm/s to 250~cm/s. We characterize the thickness profile of the central part of the film that behaves like a rubber band under tension. We show that its thickness profile is well described by a static model in which a homogeneous elastic film is stretched by its own weight. This leads to an exponential thickness profile with a characteristic length given by a competition between gravity and surface elasticity. The prefactor is fixed by the shape and area of the film, governed by the fishing line motion but also by a continuous extraction of foam film from the lateral menisci, thicker than the central part, and that progressively invades the film from its lateral boundaries. The model we propose captures the subtle interplay between gravity, film elasticity and film extraction and leads to predictions in good agreement with our experimental data.