We use grams in our shop and have not changed anything apart from the number of decimal places where the weight shows in the database.
We weigh all of our products in grams. In the products we enter 1 gram as 0.001, 100 grams is 0.100.
We then found all instances of decimal(4,2) these may be different in your version, and changed them to decimal(4,3). That should give you 3 digits after the decimal place. We could have reduced the number of digits before the decimal place but left them as they were. The main weight was found in the Products table and its easy to change using your database tool, mysql, or what ever you use.
In the shipping modules we enter weight and costs as 0.750:3.60, 2.000:4.30, There is no need for the zeros at the end but we kept them there to make things easy for us, and it could be wrote as 0.75:3.6, 2:4.3,
Then I believe that there were some instances in the shipping module language files where there were Lbs for pounds which we changed to Kg for Kilograms.
That was about all we did as far as I can remember.