spiral balance for a BetterBilt series 3740 tilt sash

A home owner from Port Saint John, Florida says:
I'm looking for 2 replacement spiral balance tubes for a BetterBilt series 3740 tilt window with a 42 lbs. 53 inch x 50 inch aluminum
sash. The original balance tube is 3/8 inch diameter and 24 inch long with a white end. I was looking at the part identifier and came up with the series 900 balance but the weights are all too low and the tip colors do not match the white tip on mine. I Called your customer service line and a very nice young lady walked me thru the identifier again and then said to send this email as it might be a custom tube.
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Bob from SWISCO responded:

Thanks for writing in. I am confident we can help, but I want to be certain we know what you're working with. Firstly, can you show me closer pictures of both ends on the balance? Secondly, 42 pounds is an awfully heavy sash weight for a Series 900 Spiral Balance. These are very skinny, and mostly used on lighter windows. The issue here may be that the plastic sheath originally around the balance tube is missing. Older Spiral Balances used a plastic sheath for the outer tube, rather than a metal tube like our newer replacements have. This means that they often become flimsy with age and fall away, as yours appear to have done. 

It's the diameter of that plastic sheath that determines what you need. Is there another balance available that has this sheath still intact, perhaps form an identical window in the house? I have a feeling its diameter is 5/8", in which case you actually would need a Series 600. But let's find out to be sure.

How to replace a tilt window spiral balance.
How to replace a tilt window spiral balance.
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How to Identify a Replacement Spiral Balance
How to Identify a Replacement Spiral Balance
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How to adjust a spiral balance on a tilt window
How to adjust a spiral balance on a tilt window
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How to choose the proper spiral balance tip color
How to choose the proper spiral balance tip color
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