Found the number J 2416 stamped on the spring.

Hello, thank you for posting,

It appears that your window uses a plain channel style like the Series 770 channel balance, but with a shoe like the 15-014. Please review the dimensions below to see how they compare. This configuration would require a custom order to assemble for you. 

Dimensions for 15-014

To further review, are you able to provide the length of the metal channel along with the weight of the window sash? The sash will need to be removed and placed on a bathroom scale. Thank you!