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I'm sorry to say that the stamps alone don't tell me anything about the window. In order to help, I need clear photos of the balances in question; specifically of the top and bottom ends, as well as any fittings, clips, or shoes that are relevant. 

Please note that it's important that we see this damage in undamaged condition and removed from the window. If any details are broken off, missing, or otherwise obscured, we will likely not be able to help.

Thank you! These look like a match for our Series 745; specifically, our S745-14 (14-1/4" long) and S745-32 (32-1/4" long).

The only thing throwing me off are your stamps. The way our balances are rated is a little different, but I'm wondering it that might just be because you have older versions. Either way, you gave sash weights so that clears it up regardless.

Based on those weight, I'd recommend the 13.25-5 for the S745-14 (13 through 17 pounds) and the 31.25-3 stamp for the S745-32 (17 through 23 pounds).

Please look these parts over and let me know if you had any questions.

Sure, I don't foresee that being an issue. Your weights may be on the high end of the given ratings, but they're still well within the bounds of their operational capacity. 

Not necessarily. The sash being droopy might have just been because the original spring had weakened over time. They only hold their tension for about a decade or so before they start falling under.

If you replace a balance with a spring that's too strong for the sash, you may run into adverse consequences there. In general the sash becomes much harder to operate since the balance is pulling on the window more than gravity. On the other hand, if this is for a top sash, then that may not be entirely unwanted.

It's ultimately up to you. My rule of thumb is to always trust in the weight of the sash and it hasn't failed me yet, but that's just my two cents.

Sure, you can actually see the weight chart on each balance store page (S745-14 and S745-32). That should hopefully give you a better idea of what your options are and what you may want to take a risk on.

Don't worry about the stamps printed on your existing balances. I actually have no idea what they mean--our balances use a more modern calibration system. Right now I'm going exclusively off of the sash weights and I recommend that you do the same. It will make things a lot more clear cut.