To further help you in identifying your tilt balance, we need to know how you attach the balance to the window. Also, how long is the metal channel, and what imprint stamped on it? We need to see the clip at the end of the cord, as well. The second photo, where your spring is attached to that rivet, is very unusual, and we want to figure out what's going on.
The channel is attached to the top of the window casing thru the hole you see in pic 1 of the metal channel.
There are two rivets on the metal channel...which is about 40" long. The third photo shows the bottom pulls which is attached to a similar rivet on the bottom of the metal channel (note the bottom pulley broke off at the rivet. the long cord from the top pulley hooks on to the sliding (rotating) lock at the bottom of the window.
I agree its unusual thus my question:)