The B777 has a pressure switch on the nose gear that measures the amount of weight applied to it.
This device is used to position the trim green band. In other words, it will tell you what CG range is available.
However it is not used to check the real aircraft weight since it is only done on the nose gear.

The DOW or Dry Operating Weight is base on figures available from the maintenance.
The plane is scaled after every C checks. A number of jacking devices are used to lift the plane and weight it.
The weight distribution on every jack is entered into a program that gives the basic weight and basic index. These figures are used to compute the DOW and DOI ( Dry Operating Weight and Dry Operating Index ).

Most European airlines use an average passenger weight to compute the loadsheet (JAR-OPS 1.620):
Male=85 kg
Female=70 kg
children= 38 kg
Infant= 10 kg
This weight includes the carry on luggage.
The check in luggage and cargo load is precisely weighted, and entered into the loadsheet program along with the cargo hold zone where it is going to be loaded.

If the job is done correctly, a loadsheet is precise within 1%.
On a 340 tons B777 this is still a 3,4 tons precision margin...