Do additional passengers impact on weight and balance of a domestic airliner?
You're really asking two questions here

1) What is the procedure (ie when are the calculations made)?

2) Do additional passengers affect the weight?

What is the procedure

As soon as check in closes, the numbers for passengers and bags is finalized - nothing else can be added to the plane, otherwise it could potentially run out of fuel. Passengers can be removed, but the captain must be informed in case it affects balance.

At this point the captain calculates the required information for weight, fuel, and balance. It's done shortly after check in closes as there is a limited window in which to add extra fuel etc - remember that the tanker needs to be long clear before the engines can be started and other departure checklists can be run.

This is done so early because the pilot needs time to prepare the aircraft for departure, he doesn't have time to mess about later on adjusting the numbers, and if he has to re-calculate later it adds a whole extra area where mistakes can be made - especially since later on the pilot is likely to be more distracted. Doing it once is fairly easy, you plug the number of passengers into a set of sums along with temperature and other related factors, and it works fuel load out for you. If you try adding passengers you have to re-calculate this, then work out how much extra to add... it's just a whole bunch of extra things that can go wrong.

Do extra passengers affect the weight/balance of the aircraft

Short answer: yes

Take an A319 as an example aircraft: empty, it weighs 40,000 kg, up to a maximum of around 60,000kg

Now I have no idea what you and your family and bags weigh, but let's produce a range. Please don't be insulted by the range: the airline aren't judging your weight when deciding if you can board late: they have to have a single rule regardless of whether it's a skinny teenager travelling alone or a party of 15 obese people


You're an adult, so you presumably weigh anywhere between 50 and 150kg 
You said children but don't state an age, so they could be newborns or adults: weight anywhere between 2kg and 150kg
I don't know how many children you have, but for the sake of argument I'll guess it's between 2 and 5 (as you said "children") - that's somewhere between 4 and 750kg


So your total weight for a single family is anywhere between 54kg and 900kg. Chances are most families are more like 250-300kg (a couple of adults at 60-100kg each, and a couple of kids at 20-40kg), but airlines have to assume worst case, otherwise their check in staff have the impossible job of deciding who's too fat to board late.

So take that worst-case scenario (6 obese people) and add a 7kg carry-on bag each, that's nearly 1000kg of weight which the pilot doesn't know on the plane. Or over 2% of the aircraft's empty weight and nearly 1.5% of the maximum takeoff weight. This is assuming they have no hold bags.

Even if your family only weighs 250kg between you and your bags, that's still nearly 0.5% of the aircraft's empty weight - a not insignificant number.

And finally you have to remember that by carrying the extra 0.5% of weight in people, the aircraft needs some extra fuel. And a bit more fuel to carry that extra fuel, and both of those extra amounts of fuel change the balance of the aircraft.

In most "normal" flights you aren't going to make a huge enough difference to balance to cause a crash, or change the fuel requirement enough to cause an issue, but if the aircraft had to divert, you could be the difference between running out of fuel or not, and in some worst-case circumstances a really big family could upset a small aircraft.