I deleted my previous post because it wasn't correct in some ways. I'll attempt to be correct here!
Here is a graphic representing the V1 speed changing with respect to weight:
Essentially, you need to remain in the lower part of the blue 'X', where I've drawn the red and green lines. If you go outside the bottom two lines that form the blue 'X', you'll be at a weight and V1 speed combination that won't be able to either satisfy the accelerate-stop portion or the accelerate-go portion. The line labeled "Continued takeoff" is the accelerate-go limit line and the line labeled "Rejected takeoff" is the accelerate-stop limit line.
This example is specifically for a fixed runway length. If you're at the red weight and would like to increase your takeoff weight to the green weight - the V1 speed can either 1) remain unchanged, 2) increase, or 3) decrease. If you had a V1 speed that was on the dashed "Balanced field Limit V1 speed" line, increasing your weight from the red line to the green line would not require a change in V1 speed. Once you figure out the balanced field limit V1 speed, it doesn't need to change if you decide to takeoff at a weight less than your balanced field limit weight.
If you were using a V1 speed that was very close to the
accelerate-go limit at the red weight, increasing to the green weight you would see the V1 speed
increase. If you were using a V1 speed that was very close to the
accelerate-stop limit at the red weight, increasing to the green weight you would see a V1 speed
decrease.