No idea what this is called

Thanks for posting. I believe this either a Series 351 or Series 390 channel balance. The only difference between these two balances is the depth of the bottom nylon shoe, or the 'heel-to-toe' measurement. See the diagram below for reference.

Comparison of the S351 and S390 balance shoes.

You'll then need to determine the length of the balance. Measure the length of the metal channel, but do not include the fittings on either end in this measurement. Finally, you need to choose a stamp option, which determines the strength of the balance. Look for a stamp somewhere on the balance channel that indicates this. If there is none or you are unsure, give me the exact weight of the window sash, and I can work it out for you.