Need 2 pairs

This looks like a 15-180 Pivot Shoe, which then connects to Series 190 Coil Balances. To know what spring weights you'll need, give me the exact weight of the window sash, and we'll work it out for you. The video below shows how to remove and replace coil balance systems. 

I am afraid I can't guess off of basic dimensions; there's too much variation in terms of glass thickness and window design to go off those measurements. Only the exact sash weight will do. Since the spring weights chosen need to total up to the exact weight of the window sash (or within 1 pound), it's actually very important that it's accurate. Otherwise, the window will fail to open or close properly. If you have a bathroom scale, lowering the sash onto it should suffice. Let me know, and we'll go from there. 

If the window weighs precisely 21 pounds, you could use (2) of the S190-540 5 pound springs on each side of the sash. This would equal 20 pounds of support overall; being within 1 pound of the actual sash weight works fine. Now, note that if you're uncertain of the spring weights on either side of the sash, it would be best to just replace all the coil springs. The spring weights must be symmetrical on each side. Let me know if you have further questions. 

Bob's not here today, but I will do my best to help.

If your windows aren't staying up, then the problem is with the balances; more specifically, the balance springs have lost their tension, which they need to counterbalance the weight of the sash. If you replace them, then your problem will be solved.

The product Bob recommended, the S190-540, is a window balance. You were informed correctly, and Bob recommended the appropriate part. If the other parts connected to the spring are in good condition then you can continue reusing them.