Window will not stay up

It definitely looks like an issue with your balance. I can see in your second photo that it's not connected to the sash, so there's nothing to hold the sash up to begin with.

Before we can identify the correct balance replacement, I need better photos of it. Please show me a clear photo of the top end, bottom end, any stamp or marking you can find, and finally the pivot shoe it connects to. Seeing it removed would be ideal but at the very least please ensure that all photos are as unobstructed as possible.