Why solar panel voltage remains rather constant while current increases?
A solar panel is essentially a diode and will generate an open circuit voltage in the 500-700 mV pr cell. Typically a lot of cells are connected in series to get a higher output voltage.

When the solar cell is hit by a photon, it makes a electron jump across the silicon junction with an energy equal to this voltage (dependent on the temperature and type of solar cell).

If more photons (more light) hit the solar cell more electrons will be released, resulting in a higher current but the same voltage.