Internetwork (IN) magnetic fields are highly dynamic, short-lived magnetic structures that populate the interior of supergranular cells. Since they emerge all over the Sun, these small-scale fields bring a substantial amount of flux, and therefore energy, to the solar surface. Because of this, IN fields are crucial for understanding the quiet Sun (QS) magnetism. However, they are weak and produce very small polarization signals, which is the reason why their properties and impact on the energetics and dynamics of the solar atmosphere are poorly known. Here we use coordinated, high-resolution, multiwavelength observations obtained with the Swedish 1 m Solar Telescope and the Interface Region Imaging Spectrograph (IRIS) to follow the evolution of IN magnetic loops as they emerge into the photosphere and reach the chromosphere and transition region. We studied in this paper three flux emergence events having total unsigned magnetic fluxes of 1.9 × 1018, 2.5 × 1018, and 5.3 × 1018 Mx. The footpoints of the emerging IN bipoles are clearly seen to appear in the photosphere and to rise up through the solar atmosphere, as observed in Fe I 6173 Å and Mg I b2 5173 Å magnetograms, respectively. For the first time, our polarimetric measurements taken in the chromospheric Ca II 8542 Å line provide direct observational evidence that IN fields are capable of reaching the chromosphere. Moreover, using IRIS data, we study the effects of these weak fields on the heating of the chromosphere and transition region.