I am an airline pilot, currently a Captain on Boeing 767 for British Airways, but I have flown most of the fleet over the years, (not Concorde) but including a 44 seat (the HS 748) and a 64 seat twinTurbo prop, the British Aerospace ATP.
As others have said, the take off weights and CG positions are mostly computed by the Dispatcher (loadmaster in the military) using a computer, but when I flew the twin prop commuter type aircraft we often had to do it ourselves.

Using a prepared form you fill in the weights of that individual aircraft, and its empty CG.
Then add the crew and pantry weights.
The loaders and check-in staff tell you the number of passengers, the number of bags, and where the passengers are seated. The seating is usually approximate - the cabin is divided into 4 sections and you get the number in each section.
Using standard weights (say 78 kg for a male, 68 for a female) you work out the effect of the passengers on the CG, then tell the loaders where to put the bags to optimise the CG (usually towards the aft end of the available range).

Sometimes with half a load of commuters (who don't carry heavy luggage) you have to move them around to get the CG right. The 748 and ATP were very nose heavy when empty. We had to put half a ton in the aft cargo compartment for an empty positioning flight. So with half a load you had to tell check-in to leave the front quarter of the cabin empty. The door is at the front so what do the lazy passengers do? They sit near the front anyway and we have to move them back to their assigned seats. And they have to stay there for the whole flight. If the aircraft is nose heavy on landing it takes quite a heave to get the nose up in the flare.
The ATP had a straight wing so fuel use did not significantly affect the CG, but on faster swept wing aircraft the CG has to remain within limits for the whole flight.

I hope that answers the question. CG is critical, even on airliners. Passengers normally tend to spread out, but a check-in plan helps distribute them evenly. Some aircraft are naturally nose heavy so you fill them from the back, and move people aft if necessary.