Window lift
Thanks for your photos. If your shoe is 1-1/8" deep then I recommend the Series 390 channel balance. This has a 19-002 top and 15-001 bottom, so as long as those match up then you should be good to go.
The only thing I'm not certain about is the length. With a stamp of 18C, the metal channel should be 19" long, not 17". Can you verify that?
Thanks for verifying! That is a bit odd but not totally unprecedented. If I had to guess, I'd say that the installers bought the wrong size balance by mistake and simply cut it down during installation. It happens from time to time.
So what I'd recommend is going with the 17" long S390-17, but with the 1630 stamp option. This carries 12 through 14 pounds, which should be perfect for a 13 pound sash weight.