channel balance ID
If you haven't already removed the balance from the window, you will need to remove one. Next, send us some photos of the complete, along with the metal length measurement of the balance. Since there are no stampings or markings on the balance, you will need to weigh your sash and get back to us with that weight number.
This looks like either a Series 380 or Series 385 Channel Balance. The only difference between these two Series is the 'depth' of the bottom nylon shoe. With the Series 380 the depth of this nylon shoe is 1", whereas with the Series 385 it is 1-3/32". Compare with your own and see what is best.
Once you know which balance Series you have, you'll need to select the right length. I'm afraid I can't really read the length of the metal channel in your photos. Measure the length of the metal channel, not including the nylon attachments at either end, to obtain this measurement.
Finally, once you know your balance Series and required length, you'll have to select a stamp option. The stamp option reflects the balance's spring calibration, or the weight it is meant to support. You say your window weighs about 20 lbs; be sure to weigh your window sash on a scale. You want to be as precise as possible; if you select a stamp option that is too weak, you'll have difficulty opening your window. If it is too strong, your window will tend to slide open. You want the stamp option to be just right.