Powder is always referenced by weight, not volume, a grain is a unit of weight... but powder is often dispensed by volume... there in lies the rub!
Where things get tricky is that most powder measures (not scales) measure by volume in cc's. To convert between weight (grains) and volume (cc) you need to cast your mind back to high school chemistry where they taught you that density equals mass (we will use mass and weight interchangeably... I know they are not the same... but they are close enough for our purposes) divided by volume.
Once you know the density of a powder, you can easily convert back and forth between weight and volume.
Where do you find the density of powders you ask? You look at the file which I have attached wherein you will find density, and its inverse "bulk" for most major powders.
While volume and weight are proportionally related through density, WEIGHT ALWAYS TRUMPS VOLUME WHEN DETERMINING CHARGE. That is why you check every few powder drops on your scale to ensure that the volumetric measure is throwing the proper WEIGHT.
Now, on to your question... I have used the Lee dippers in the past, and they are marked with their volumetric measurement in cc's. The dipper marked 0.7 holds 0.7 cc's of powder, which should have a specific weight given that powder's density. If you are getting large discrepancies, between what a given volume of powder should weigh, and what it does weight, you have to isolate and examine each variable. Is the volume actually what you think it is? Is the powder density correct? Is your scale working properly.
Let's look at an example using Alliant's Unique...
The powder density chart shows that Unique's density is 9.158 grains/cc, so if you use a Lee Dipper that holds 0.7 cc's, you weight should be 9.158*0.7 = 6.41. If we look at the Lee Dipper chart, we see that indeed a 0.7cc scoop of Unique should weight 6.4 grains. It works in reverse too... imagine you were using a volumetric measure, and you wanted to use 3.5 grains of Unique in some loading, where should you set your volumetric measure? Simply divide 3.5 grains by 9.158 grains/cc. Units of grains cancel each other, and you are left with 0.38218 cc's. Check your work, whats 0.38218 multiplied by 9.158 grains /cc? Yep, 3.5 grains. Keep the dimensional analysis straight, and you can't go too far wrong... but ALWAYS CONFIRM VOLUMETRIC MEASUREMENTS WITH A GOOD SCALE!
Hope this helps... remember volume may be easier when loading ammo in bulk, but charge weight is the gospel.
Good Luck