  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 (SST) and the
\textit{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 $1.9\times10^{18}$,
$2.5\times10^{18}$, and $5.3\times10^{18}$~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 \ion{Fe}{1} 6173 \AA\/ and \ion{Mg}{1}
b$_2$ 5173 \AA\/ magnetograms, respectively. For the first time, our
polarimetric measurements taken in the chromospheric \ion{Ca}{2} 8542 \AA\/
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.
