The question of whether to use weight or volume when making honey bee supplemental feeds is a common one. The answer—it doesn’t matter—is confusing to people so here is a short explanation.
1 cup of refined sugar = 200 grams = 7.05 ounces = a little less than 0.5 pound.
1 cup of water = 236 grams = 8.3 ounces = a little more than 0.5 pound.
For the purposes of making sugar syrups for honey bees—either fall syrup (2:1) or spring syrup (1:1)—the numbers are close enough that you can assume that 1 cup of water or sugar equals 8 ounces of water or sugar. You can mix up the measurements freely. For example, you can measure 1 pound of sugar (about 2.25 cups) and 2 cups (about 1 pound) of water for 1:1 syrup.
Yes, these are only approximations. But the point to remember is that we (humans) are making syrup for them (honey bees.) Honey bees, as it turns out, do not have a recorded system of weights and measures. A little bit more or less sugar per volume of water will not bother them. In fact, the nectar that they collect in the field has an infinite range of sugar-to-water ratios.
The rationale behind using the two different ratios is simple. Spring syrup is similar to nectar, and the availability of nectar stimulates the production of brood in the spring. So by feeding light syrup in the spring we coax the workers to build comb and the queen to lay eggs. On the other hand, fall syrup more closely resembles honey and bees tend to store fall syrup for winter.
But again, these proportions are only approximations and there is nothing magical about them. The ratios are no more natural to the honey bees than eating refined sugar.
The moral of the story is this: relax. Your approximation will be close enough. However, if you are one of those types who absolutely must carry out your calculations to the fifth decimal, I highly recommend a little program called convert.exe. I use this little tool constantly. It will convert virtually anything to anything else, and it is quick and easy to use. You can find it here.