A SWR meter will vary in swr with coax length if unbalanced as your coax length is around 1/2 wave length multiple.
I have never seen an SWR measuring device that was designed to be used with a balanced load. This could certainly be done, but such devices are usually intended to measure SWR on a coaxial, i.e., unbalanced, line.
For the purposes of SWR measurement, the feedline is part of the "load." The load attached to the SWR meter includes the feedline and everything attached to it; e.g., antennas, splitters, stubs, etc. A properly designed and operated SWR meter will correctly measure SWR regardless of the load.
In general, the SWR at the shack end of the feedline will not be the same as the SWR at the antenna. Feedline loss attenuates the driving signal as it travels forward along the line, so the signal available to be reflected at any point is reduced. Similarly, feedline loss attenuates the reflected signal as it travels back along the line, reducing the signal available to be detected by the SWR meter. In general, feedline loss reduces the SWR observed at the shack end of the feedline.
In addition to loss, the transmission line changes the phase of the incident signal traveling forward along the line and the phase of the reflected signal as it travels back. The incident and reflected signals are superimposed on (i.e., add to) each other at every point along the line. At some points, the incident and reflected signals will tend to reinforce each other, while at others they will tend to cancel each other. These reinforcing and canceling effects produce the standing waves we measure.
The effects of loss and phase can be seen by plotting the impedance along a transmission line on a Smith chart:
The SWR at the 1K$\Omega$ resistor is 20. Traveling 60$^o$ toward the generator on RG58/U coax, the impedance changes dramatically to 5.9-j31 $\Omega$ and the SWR is about 11.7; 45$^o$ further toward the generator, the impedance changes to 9.4+j13 $\Omega$ and the SWR is about 6.2; completing the half-wavelength journey toward the generator, the impedance changes to 257-j0.6 $\Omega$ and the SWR is about 5.1. (Note: the small differences in distances along the transmission lines are a consequence of the parametrized model used.)
This tool also shows that, of the 1.00-W incident on T3, only 0.247-W arrives at the 1k$\Omega$ resistor, representing about 6.1-dB of loss. By comparing this loss to what would be lost on a matched line (resistor = 50-$\Omega$), we see that more that more than 77% of the loss is a result of the large mismatch.