Kohls's tr337
Hello! Hopefully I can help with this project.
What you're showing me in your photo is the top cap of the balance. Yours specifically is an old style "crossbow" balance, which is not something that's made anymore. These have fallen out of use, so you will need to use a modern style equivalent to work in its place.
To clarify, if your window won't stay up, then it's a problem with the entire balance, not just this plastic part. You need to replace the entire assembly.
Before I can recommend a modern replacement, you'll need to remove an undamaged version of the balance assembly and show me a clear picture of the top end, bottom end, shoe, and the hook or clip at the end of the cord. I want to stress that an undamaged version is 100% necessary as a reference. You won't be able to know what you need without one; due to how they're designed, they're next to impossible to ID once they break and come apart.
Lastly, you will need the precise weight of the sash, down to the ounce.