Lateral balance is not calculated as everything in the fuselage is close to the centre of gravity and any imbalance there can be trimmed out easily. There are limits for fuel imbalances in the wings though.
Most airlines use an averaging system approved by their regulatory authority, which will stipulate an average per person, checked bag and carry on. The weight per person may be refined on the basis of season (winter/summer), and male/female. If the average weights are obviously not going to work - say a charter for a football team, then individual weights should be used. Average weights may not work very well on smaller aircraft because of the small sample.
Freight is always weighed.
The weight of an airliner is calculated for takeoff and landing - to the lb/kg. After we start engines we work to the the smallest unit on the fuel gauge - usually in hundreds of lb/kg.