Identifying what channel balance I need

I'm afraid that there's no way to identify what balance you have without seeing the old one. If this window is missing its balance, then you'll have to check to see if you have an identical window elsewhere in the house that uses the same hardware. Without a reference, it will be exceptionally difficult to identify the right match.

That will make things a lot harder. I'm afraid the only thing we can do at this point is guess.

I see you have a take out clip, at least, and based on the top sash guide it may be reasonable to assume that you have a 1/2" wide non-tilt window channel balance, perhaps something like our Series 385. I can't guarantee that this would work, but it's potentially a place to start.

If you're willing to try it out, let me know the height of the visible glass and the exact weight of the sash and we can try to estimate the right size and strength.