That counterweight is on the end of a strait rod. The one in the sprite is of a different kind.
As you can see in the attachment the counterweight is not directly on the rod, but is on a rod, which can rotate around the main rod (or however you describe it). Once the switch is turned the other way, the counterweight will turn 180° around the main rod and then 257 would look like 256. (no, I didn't find any on youtube being used, hence the still image, which were hard enough to find)
This type is much harder to remote control because it's not enough to just turn the main rod. You have to manually turn both the rod and the counterweight. I have never seen it done and I think it would be much simpler, cheaper and more reliable to just replace the whole thing with a standard electric engine used everywhere else.
Why the different types: well one issue people usually fail to realise is that an important feature of a switch is how hard the moving part presses against the stationary part. Generally speaking the more you can be sure that the switch is in the right position (and not say 1 mm off) the faster a train can travel on the switch in question. Different placements of the counterweight gives different parameters when it comes to issues like this.Clickable link to image source page