Current in parallel circuit not increasing linearly
Your assumption that the current would rise linearly would only hold if the solar cells did not have any output impedance, or generally if the load has a much smaller impedance than the solar cell's output impedance.

In other words, the actual situation is actually roughly something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

Part of the actual generated current will go through the equivalent output resistance \$R_{solar}\$ instead of through the load.

When adding one more solar cell, the output resistance of the solar cell will become halved, as it is shunted with the other solar cell. Like so:







simulate this circuit

Using \$N\$ solar cells, will indeed give rise to \$N\$ times the current, but it also makes the shunted output resistance \$N\$ times lower, causing more current to be "stolen" from \$R_{load}\$.

You can actually calculate this influence if you assume all solar cells have the same current and output impedance. You would get:

$$I_{out} = \frac{N\cdot I_{solar}}{N\left( \frac{R_{load}}{R_{solar}} \right) + 1}$$



(Fit result: \$\frac{R_{load}}{R_{solar}} \approx 0.24\$ and \$I_{solar} \approx 9.14 A\$)