I have only weighed grains once... on a fancy digital scale at work.
1 kg of whole pale malt is 1.72 liters
1 liter of the same weighs 586 grams.
Knowing this I measure out all grains by volume in a 1 liter finely graded pitcher. I find this accurate enough. I guess certain speciality grains will differ from the base grain in their volume/weight ratio but the differences will be negligible.
The hops I weigh very accurately on a digital powder/reloading scale because I had that one before I started brewing.