No doubt the recipe writer intended the liquids to be by volume, but once again, there is a correspondence. The gram has, in recent times, been attached to a more stable standard, probably mostly for the benefit of scientists, but by original definition a gram is the weight of a cubic cm. of water at sea level at 4 deg. C, so a cc is a gram, a liter is a kilo. Similarly in standard weight a liquid ounce of water is one oz. by weight (presumably also at sea level).
As a diabetic who must follow a strict diet, which I hate, dry ingredients are by weight. Liquid ingredients are by volume. If you have any type of stomach reduction surgery, this is VERY important as after 1 year your stomach will only hold 1 egg. So getting the correct amount of protein, for an adult usually 50 to 60 grams a day, is very important when your stomach holds so little volume. This is how I do it. And yes, some cooks will interchange things sadly. Then I email them about how a diabetic nutritutionist does things. Dry by weight, wet by volume. Simple, no?
The recipe is listing weights for dry and liquid ingredients. If a liquid or dry ingredient is being listed in terms of a measure, for the US, it is expressed as cups or portions of cups. Some liquid measuring cups will also show measurements in terms of liquid weight- ounces and milliliters. Cups for dry measures usually don't show a weight measure, because 1 cup of a dry ingredient will vary in actual weight depending on what the ingredient is. A cup of rice weighs more than a cup of mashed potato flakes, for instance. Tablespoons and teaspoons can represent dry or liquid measurements, usually for very small amounts of ingredients which would be more difficult to weigh. Their exact measurement usually isn't that critical, and a few minute milligrams or drops won't matter much.
The solid ingr. are clearly weight; an oz. of water-or butter- is an ounce by weight or volume, so no worry there. The brown rice syrup is probably volume, but that should be very close by weight or volume also
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