Coil balance and pivot shoe
Thanks for posting. Looks like you have a 15-111 Pivot Shoe, which works with either the 1/2" wide Series 160 Coil balance springs or the 3/8" wide Series 165 springs. You'll need to remove your old balance mechanism and measure the width of the springs to see what matches best. The video below shows how to do this.
For coil balances, the spring weights needed for each new coil spring is actually determined by dividing the sash weight in half. See the video below. So if your window weighed 15 pounds exactly, and you knew you had the 1/2" wide Series 160 springs, you could use two of the S160-07 7.5 pound springs, one for each side of the sash. This would give you 15 pounds of overall support.