Effects of ground plane size on antenna gain
I am no RF expert, but I do know as you change the ground plane size you change the field distributions at the edge of the antenna. 

Thus, if you keep your feed point in the same spot the impedance will have changed due to the field distribution change. Because the impedance changes, the antenna will no longer be in the sweet spot (the 50 \$\Omega\$ spot), meaning that it will suffer impedance mismatch loss. 

Therefore, as you increase the size of your ground plane, you need to redetermine where to feed the signal so as to minimize impedance mismatch loss.