Replacement coils, etc

Thanks for posting! The piece you have pictured here appears to be the 15-186 Coil Balance Clip. It is used along with the 15-180 Coil Balance Shoe. To confirm that this is the correct replacement, you will need to remove the shoe and carefully compare the dimensions.

Alternate image for 15-180

The compatible coil springs are the Series 190 Coil Balances, secured to the shoe using the 33-073 #8 x 1/2" Truss Head screw. To determine the spring strength needed for the window, you'll need to remove the coil springs and check for any stamps/markings. 

If there are no stamps/markings or they are hard to read, you'll need to obtain the exact weight of the sash. Once you have the sash weight you'll need to divide it by the total number of coils in the window. For example, if your window ends up weighing 12lbs, you'd need (2) 6lb coils. So you would need the S190-640.