I agree that measuring spoons are intended to measure volume and not weight.
That's the exact reason why I used two separate ingredients, sugar and water, to prove that the gram weights will indeed be different.
I used ingredients with known weights - 1 cup of water weighs 8 oz, and 1 cup of sugar weighs 7 oz. Divide both of those by 16 to get the respective weights of 1 tablespoon.
Sugar is the easiest ingredient to use as the control, it always measures the same, as long as you level it off. Unlike flour, where the weight will vary depending on how much you pack the spoon or the cup. Flour can weigh anywhere from 4 to 5 ounces, depending on how you put it into the cup. Even water can differ, since it depends on how you account for the meniscus (see link).
Using the scale made it easier to quantify the difference between the two spoons. The smallest unit of weight measurement is 1 gram. The smallest unit of volume measurement is 1/4 teaspoon.
I do use my scale for all of my baking, but I still need the measuring spoons for the small ingredients.
But that still doesn't guarantee success when trying a new recipe. It depends on what tools the recipe developer used!
I keep a conversion chart on my flour container. I converted the various cup sizes (1 cup, 1 1/3 cup, 1 1/2 cups, 2 cups, etc) to weights. I used 4.5 oz per cup as my conversion factor.
However, if I use certain sources of recipes, that conversion doesn't work, and I need to use 5 oz as my conversion factor. (Better Homes and Gardens appears to use 5 oz cups of flour.) So now I keep both sets of conversions on the flour container.
If you buy a new baking book, it'll usually tell you the method they use to measure flour - "dip and sweep", "scoop and sweep", "spoon lightly into cup and sweep", etc.
But if it's a recipe that your grandma got from her neighbor's cousin, you'll have to figure out what method they used for measuring flour to guarantee success, no matter how accurate your scale is!
http://chemistry.about.com/od/chemistrylabexperiments/qt/meniscus.htm