Weighing Coins.

Check the specs for your weighing device regarding accuracy, repeatability, return to zero, linearity, drift and resolution. Your scale or balance might not weigh very light items as good as heavier items. In my case, to weigh dimes, I would use the scale that's too small to weigh a silver dollar. Can you say your make and model number of what you are using to weigh?

In the past I've purchased several scales. They just sit. Just don't have time to weigh coins I guess.

This brings to memory a comparison I did on mint state and well worn 10 cent pieces, quantity of 12 in the group. For what it's worth I found the difference between pristine and worn out be a ballpark 2% weight. For the OP to say a dime varies by one-third of a gram something else isn't adding up right to me. That's almost 5 times the variance I saw. Just for discussion if a dime was one-third gram more or less, that equates to about a 12% difference. I was seeing a worst cast of about .05 or .06 grams difference. His deviation seems to be more frequent instead of an outlyer if I read the text right. I suspect something is not quite right in the measures or user or equipment. Unless of course the OP comes back maybe realizing some sort of oversight or error someplace in his findings.