As you said, it is only the V1 and VR that are different, V2 is unchanged.
V1 cannot be lower than Vmcg for obvious reasons, so often, especially at low speeds as shown in your example, V1 is limited by the Vmcg speed. If the aircraft has a higher thrust setting, Vmcg will increase and therefore V1 must also be increased.
This explanation would explain the changes to V1 at the lower weights and speeds, but not the higher end. Therefore maybe there is another difference between the two aircraft such as the brakes used by each operator. A better brake system would change the Accelerate Stop Distance Required, and therefore alter V1.
VR is chosen as a suitable speed that is equal to or greater than V1 but less than V2, therefore if V1 was increased, VR would also increase.
Finally V2 is defined by aerodynamic considerations, therefore would not have changed with the higher thrust setting.