Spiral Balance Springs of Unknown Origin

These are a pair of balance springs I've taken out of a tilt-out single-hung unit. These are windows in a modular home of decent quality.

The aspect of these balance springs is that they have black tips instead of any of the colors I can find on the internets. This tells me that either there were no sizing standards when these were manufactured, or that they were manufactured at a location that didn't participate in the sizing standards.

I have found balance springs of seemingly the same size: 3/8" dia x 29" long. That's not the issue, I'm more concerned about making sure I get the right weight rating...