Sunspots are the most spectacular manifestation of solar magnetism, yet 99% of the solar surface remains "quiet" at any time of the solar cycle. The quiet sun is not void of magnetic fields, though; they are organized at smaller spatial scales and evolve relatively fast, which makes them difficult to detect. Thus, although extensive quiet Sun magnetism would be a natural driver to a uniform, steady heating of the outer solar atmosphere, it is not clear what the physical processes involved would be, due to lack of observational evidence. We report on the topology and dynamics of the magnetic field in very quiet regions of the Sun from spectropolarimetric observations of the Hinode satellite, showing a continuous injection of magnetic flux with a well-organized topology of Ω-loop from below the solar surface into the upper layers. At first stages, when the loop travels across the photosphere, it has a flattened (staple-like) geometry and a mean velocity ascent of ~3 km s-1. When the loop crosses the minimum temperature region, the magnetic fields at the footpoints become almost vertical and the loop topology resembles a potential field. The mean ascent velocity at chromospheric height is ~12 km s-1. The energy input rate of these small-scale loops in the lower boundary of the chromosphere is (at least) of 1.4 × 106-2.2 × 107 erg cm-2 s-1. Our findings provide empirical evidence for solar magnetism as a multi-scale system, in which small-scale low-flux magnetism plays a crucial role, at least as important as active regions, coupling different layers of the solar atmosphere and being an important ingredient for chromospheric and coronal heating models.