Single hung block and tackle 1/2 inches by 27

Thanks for reaching out! Your channel balances looks like they could be either the Series 380 with a 1" shoe or the Series 385 with a 1-3/32" shoe. To determine which series you have, you'll need to carefully compare the dimensions for the depth of your bottom shoe. Take a look at the diagram below for reference.

Comparison of the S380 and S385 balance shoes.

Once you've confirm which balance series you have, you'll need to confirm the stamp/markings from the metal channel. May I see a photo of those stamps? 

If there are no stamps/marking on the channel, I'll need to know the exact weight of the sashes these balances are installed in.