The dosage quantities for dry chemicals are almost always by weight. This is because the density of dry chemicals varies and simply tapping a measuring cup can have the contents settle. As you correctly point out, for liquid chemicals the dosage quantities are usually by volume.
Fortunately, for Dichlor, the density is such that roughly speaking 1 ounce weight is approximately 1 ounce volume. For non-chlorine shock (MPS), 1 ounce weight is around 3/4 ounces volume (your particular product you measured is a little more dense -- one ounce weight being 1/1.6 = 0.63 ounces volume). For baking soda (Alkalinity Up), 1 ounce weight is 0.8 ounces volume. The measured dry bulk density of some common pool/spa chemicals is shown
here.
As you've discovered, it's a good idea to at least initially use a kitchen scale to determine the actual density of your specific product you use. After that, you can dose by volume if that's easier for you.
And remember that there are 2 tablespoons in an ounce of volume, 3 teaspoons in a tablespoon, so 6 teaspoons in an ounce of volume.
Richard