That is probably because of the default box size. We automatically set a box size of 12" square, which has a minimum effective weight of 5 lbs.
To correct that issue, go to the page:
Find the FedEx shipping area and change your box dimensions to 12x10x3... or something smaller like that. The rates will then be more accurate for small shipments. If you can't find the correct lines to update, attach a copy of the page to this thread and I'll give you line numbers.