Identifying replacement spring

Hello there. This looks like a 15-177 Pivot Shoe, which works with Series 152 Coil Balance springs. Unfortunately, knowing whether that spring stamp is a '6' or '9' is quite impossible! Could you double-check the sash weight? Be as precise as possible. That should narrow down what spring weights you require.

If the sash weighs exactly 16.6 pounds, I would actually recommend the S152-8 8 pound spring, one for each side of the sash. That would give you 16 pounds of overall support (being within 1 pound of the exact sash weight works just fine). 

The fact the old springs apparently either were for 6 or 9 pounds apiece is a bit strange then. Those weights would either be too weak or too strong for the window. Did you ever have trouble keeping the window open or closed prior to the springs breaking? Either way, since it's unclear what the right way of reading the stamps are, going by the sash weight is the best solution here. Just double and triple-check it to be safe.