Thank you! Okay, so with this data in mind, my recommendation would be the S385-19 channel balance with an 1820 stamp option. Let me break down the logic of this pick.
Number one, this style of balance is very common in windows like yours, especially the top and bottom nylon fittings. I believe the top fitting, the 19-005, will be compatible with your top sash guide. The 15-004 bottom fitting, however, is another story. It is a relatively large shoe, so there is a chance that it is too big to fit in your channel. What this means is that when you open and close your sash, these bottom fittings will dig into your track on either side and cause damage. It's very important that you keep this in mind! If you install these balances and find that they're too big, don't try the sash. Instead, remove the balances and shave the 15-004 down a little, by about 3/32". That will give your sash the room it needs to operate.
On the other hand, the big shoe may be exactly what you need and this won't be something you have to worry about. It's simply not possible to know. Better to shave down a large shoe if necessary than pack out a smaller shoe, which probably isn't possible to begin with.
One other thing to note is that the S385-19 has little tabs on both the top and bottom nylon fittings. These may get in the way of operation, but if that's the case then you can just snip them off.
Finally, the 1820 stamp option carries 8 through 12 pounds, which should be fine for your sash weight.
Please note that I cannot guarantee that this will work for you, it's simply my best guess. I have no idea if it will work or not. Also note that balances altered in any way, like by shaving a shoe down or snipping off tabs as previously suggested, cannot be returned for a refund. See our return policy here for more information. These may be necessary for the balance to work, but they would also invalidate your ability to get a refund. If you have any other means at your disposal to figure out what these balances are without needing to guess, I highly recommend pursuing it.