Thanks for reaching out! Your window balances appear to be an older, discontinued Arrow Balance. The good news is your balance can likely be replaced with our Series 770 Balance made with a terminal clip.
To determine the correct replacement, I'll need to know the length of an undamaged balance. This measurement is from the top of the black nylon tip to the bottom of the beige nylon tip. I'll also need to know the exact weight of the sash to determine the stamp option your replacement balances would need to have.
Your pivot shoe appears to be the 15-129 9/16" Thick Pivot Shoe. To confirm that this is the correct fit, take a look over the dimensions and compare them to your shoe.
I'm glad to hear the dimensions were a match. You'll need the S770-32 to replace your balance.
Regarding the stamp option, if you've rounded up to 20lbs, I suggest using the 32B (supports 14 to 20lbs); if the sash is slightly over 20lbs, I suggest using the 32C (supports 20 to 25lbs).
