broken coil balance spring

Hello!

I agree that the Series 150 coil springs look close but I'd like to see a photo of the pivot shoe removed from the window to confirm. 

As for strength, you'll need to weigh the sash on a scale and then divide the weight by the total amount of springs in the window. 15 springs for a single window is a very, very high amount and you typically only see 2-4 on a window like this; that is, 1 to 2 on each side. Just something to keep in mind.

I'm afraid this isn't the pivot shoe. The pivot shoe should be located below the coil springs. I'm also a bit confused about the weight you gave. Are you saying that the window sash weighs 4 pounds? Or is that just the weight for one coil spring? You can always check the band of the spring for a stamped code that would indicate the spring weight.