Tilt Windows Need Plastic Pulley Piece
This looks like part of the pulley system for the balance. I'm afraid there's no way you can replace this. You'll need an all new balance. I'm surprised it was damaged by the sun at all, these should be completely obscured from the sun when installed. Were these pulleys facing out? If so, then these balances were installed backwards.
We can supply a replacement balance for you, but we'll need more information. I'll need a clear picture of the top and bottom of the balance, a picture of the stamp, and a picture of the clip or hook or shoe (or whatever) is at the end of the cord. I recommend using an undamaged version of this balance as a reference, assuming the one on the other side of the window is in good condition.