How do I move more than 128 pixels when using Arduino Leonardo's Mouse.move?
The USB HID protocol for mouse is the limitation on sending more then a byte sized value for the mouse movement in one event.

You can't create a faster USB mouse. Repeat the call of the move() function. Of course you can use a function to call move() repeatedly to move to target destination.

void mouseMove(long x, long y) {
  long max = max(abs(x), abs(y));
  int count = (int) (max / 127);
  signed char stepX = x / (count + 1);
  signed char stepY = y / (count + 1);
  for (int i = 0; i &lt; count; i++) {
    Mouse.move(stepX, stepY);
  }
  signed char resX = x - (stepX * count);
  signed char resY = y - (stepY * count);
  if (resX != 0 || resY != 0) {
    Mouse.move(resX, resY);
  }
}