My replacement scale arrived today.
The counterweight, a ball bearing, measured 0.437" (7/16") and was non-magnetic.
I reckon I am in the market for a single ball bearing. Somebody pointed out that I might be able to economize by buying some 7/16" slingshot ammo at the local hardware store and sorting to get exactly the weight I need.
Oh, the joys of having more time than money!