I've been weighting some my silver eagles and they all seem to be 31.7 grams. I know they should weight 31.101, but is this normal for them to weight over. One I bought from a dealer, another I did a trade on.
Have you checked your scale? Do you zero it before weighing a coin? Have you weighed other coins? (If so, do the weigh properly or do they also weigh a bit over?)
Reading zero with nothing on it doesn't mean a thing. Sometimes I will use a container and zero its weight out and measure again and compare.
If you look on the certificate of authenticity (Mint), under the heading "weight" is listed the actual weight of the coin followed by +/- which indicates to me that the weight on these is not always consistent.........
If you're still that worried about it, take those same coins to another scale and see if it weighs the same. If they are off, then you know it's your scale.
from other posters and checking a bunch of my ASEs they tend to run over the 31.1 but mostly just a bit; 1-2.5 tenths
Your scale should have a calibration weight that came with it, and a method of recalibrating the scale to match that weight. You might want to try that. Being 6 tenths off (over half a gram) is not normal. If nothing else, you can always check your scale by taking one of the ASE's to a jewelry store and have them weigh it. If it matches your scale, all is good.
ASE is 99.9% silver and 0.1% copper. Silver is a very soft metal, and copper is alloyed with it to strengthen it. In order to contain exactly one troy ounce of pure silver, the total weight of an ASE must be more than one troy once.
Since the government guarantees the coin to have one oz of pure silver in it, they tend to make them just a hair heavy to make sure there are no underweight pieces out there. Six tenths of a gram seems a little much but I would think it would be OK.