I have 2 scales, a Jeweler's scale I bought for like $20 on ebay which I use to weigh individual eggs (is accurate to 0.01g) and a kitchen scale from Salter, which is accurate to 1g, which I use for weighing entire trays of eggs (48 at a time, the scale goes up to about 4Kg), which I bought via Air Miles. I also use the jeweler's scale for grading.
A digital bathroom scale would be good enough if you can make it give you readings in grams. They may or may not be your native measure, but if the scale will report in grams its a much finer value than ounces.
FWIW, I set 96 eggs weighing a little more than 6Kg at setting time. My desired weight loss is ~50g/day, so you need a scale that can be accurate with small amounts.
BTW, an average egg is ~60g.