In the United States, a drone that weighs 55 pounds or more needs to be registered using a different process than lighter drones. What counts towards that weight -- is it dry weight, fueled weight, maximum takeoff weight, or something else entirely?
Unmanned aircraft weighing less than 55 pounds and more than 0.55 pounds (250 grams) on takeoff, including everything that is on board or otherwise attached to the aircraft and operated outdoors in the national airspace system must register.
I find this compilation of regulations by UAV Coach very helpful:
It is categorised first by each US state then wider into other countries in the world.
For example, the rules for the mass of a drone in Florida is
To fly a drone as a hobbyist in the state of Florida (i.e. for fun / pleasure) you are required to follow the FAA’s recreational model aircraft rules. One of those rules is that if your drone weighs more than 0.55 lbs (250g), you’ll need to pay $5 to get it registered over here. And there are additional rules when it comes to airspace and altitude, keeping your drone within line-of-sight while you’re flying, and more.
(I know you've asked about the FAA, but I post this to help others)
In the UK, the CAA have the following definition:
A small unmanned aircraft is defined as ‘any unmanned aircraft, other than a balloon or a kite, having a mass of not more than 20 kg without its fuel but including any articles or equipment installed in or attached to the aircraft at the commencement of its flight’.
(This creates an apparent inconsistency, in that batteries count towards the maximum mass while liquid fuel doesn't - but, as the mass of a battery changes negligably with charge, you can think of the battery as the fuel tank and the charge as the fuel.)
Most weight requirements refer to AUW or 'all up weight'. This is everything strapped the unit to make it fly. In most electric powered models, the battery can make up nearly half the total weight of the craft. (if it's a quadcopter. Airplanes, maybe somewhat less.) But one should assume the battery as part of the overall weight measurment for licensing if you're going that route.