For passenger weights, a typical airliner will use standard weights. Flights are also divided depending on short-haul and long-haul. The standard weight for a long-haul flight in my company was 81kgs. For short-haul it was 84(or 85)kgs. The rationale is that passengers tend to carry more hand-luggage on short flights and the passenger weight is meant to cater for passenger AND carry-on bags. It may seem pretty hit and miss but additional 10kgs per pax for 400pax will mean an additional 4000kgs spread throughout the cabin.. Thats a big amount but the since the aircraft weighs 350-400 metric tons it's around 1 percent. And that 4000kgs is only if everyone exceeds by 10kgs, it probably is much less as some will be over and some will be under.
Staff are supposed to look out for groups of large pax which do not fit the standard weights (think Sumo wrestling team or oompa-loompas attending a conference) and in such instances a correction is made in the load-sheet with estimates.
The short-haul weights will also change with season..factor in heavier winter clothes for that.
For distribution most check-in systems (or departure control system-DCS) have a built in logic which distributes the seats evenly unless there is intervention by the check-in agent to change the seat. In some cases the ground staff may block seats to achieve a decent trim (Balance). For example on a smaller commuter aircraft with one door for boarding (ATR 72) all passengers will want to sit in the rear of the aircraft in order to be near the door (boarding-door at rear) and be first off the plane. Since they are so much in a hurry to get off the plane they usually have only carry on bags. This means that the front of the plane has less pax and there is not much that can be loaded into the forward hold to balance the bunch of pax at the rear. In such cases the ground staff may decide to pre-seat the passengers evenly along the cabin and block other seats to ensure that a decent balance condition is met.
In flight the movement of passengers used to be managed by 'trimming' the horizontal stabilizer. With the 747-400 and MD11 the designers introduced the tail-tank where fuel was stored in the stabilizers (I think 10,000kgs for the 747-400, MD-11 less I think around 7,000kgs)
Some aircraft are a challenge to trim well, a good example is the 747 combi. With a full maindeck and light passenger load you will face problems with the aircraft exceeding the rear limits (tail too heavy) unless the guys in the warehouse loaded the really heavy freight on the lower-deck pallets which the weight n balance guy can plan for the forward hold. It got so bad that sometimes we had to upgrade pax to business class (in the nose) to achieve a legal trim..we're talking 10-20pax here, not one or two.
Not related to the original question but the catering loaded will also play an important part of the calculation. A B747-400 taking off from London to Singapore will be stuffed to the gills with food and drinks for 400 pax but for a shorter sector there will be a lot less carried. These data are in weight-schedules the weight and balance guy will use in preparing the weight n balance document.