Setting the tonearm height doesn't have anything to do with balancing the counterweight. Balancing the CW, you set the tracking force to 0, then adjust the CW so the tonearm "floats" in the air, and stays there. Then after you set the tracking force and set the needle on the record--still with the turntable unplugged from the wall--adjust the tonearm height so the tonearm is parallel to the record. For most cartridges, this'll be very close to the correct cantilever angle.
You don't need the Dual alignment tool, the appropriate record protractor works better actually, but the Dual tool is a decent approximation, I think. It's actually just a plastic piece that slips over the end of the cartridge holder with a V indicating where the stylus should be.