Coil spring support covers
Thanks for your post. The while plastic piece is the coil balance support. It appears this is made to house three coils. The coils are fairly damaged, so they will need to be replaced as well.
Be sure to double check the shoe and the other hardware in the window to determine if they need to be replaced.
The support reminds me of the 15-205 Triple Coil Support, which is used with the 3/8" wide Series 165 Coil Balance. To select the correct coil weight options, you'll need to look for a stamp/marking on the existing coils. If there are none, or they are hard to read, please see the tutorial below this thread.
We show different assemblies in the tutorial but the steps are the same.