If ALL your weights are currently expressed in GRAMS, and the DIGITS used are whole numbers, then you can run a SQL PATCH that will DIVIDE all your product weight values by 1000.

When you have done this, you will need to edit your english.php LANGUAGE FILE to change the LABEL for your weight unit from g to kg.

SQL patch:

UPDATE products SET products_weight = (products_weight / 1000);

You can run this through your ADMIN >>> TOOLS >>> INSTALL SQL PATCHES