The standard mixtures are 1:1 in the spring and 2:1 in the fall (sugar:water).
Weight or volume? Both a pint of water and a pint of sugar (about 2 and 1/3 cups) weigh about a pound, so it really does not matter how you think about it. At least until you have mixed the syrup. So if you take 10 pints of water, boil it, and add 10 pounds of sugar you'll get the same thing as if you took 10 pounds of water, boil it, and add 10 pints of sugar.
The next confusion seems to be on how much it takes to make how much syrup. The volume of 10 pints of water and 10 pints of sugar will make about 15 pints of syrup, not 20. The sugar and the water fit together. Sugar tends to come in four-pound bags now, and half a gallon of water weighs 4 pounds, life is easy to make 1:1 syrup. For 2:1, a four-pound bag of sugar is added to a quart of boiling water and stirred until dissolved.
Don't confuse the issue of how you measure. Measure before you mix. In other words, you can't fill a container 1/2 of the way with water, and add sugar until it's full and have 1:1 syrup. You'll get more like 2:1 syrup. Likewise, you can't fill it 1/3 of the way with sugar and then add water until it's 2/3 full and have 1:1 syrup. You'll get more like 1:2. You have to measure both separately and then put them together to get an accurate measurement.
How to make syrup.
I boil the water and add the sugar and then when it is all dissolved turn off the heat. With 2:1 this can take some time. Either way, boiling the water makes the syrup keep longer by killing all the microorganisms that might be in the sugar or the water. Allow to cool completely before you put on bees.