It may seem very difficult now but I did everything you say, manually.
Set up loadsheet in advance of a/c arrival.
1. A/C registration gives weights including pantry equipment/catering for that route. May not have been extremely accurate but today isn't either (see below).
2. Forecast of freight and pax numbers allows you, as traffic officer/despatcher, to create load plan. Usually dead standard (all the bags in the back lads), freight in the front or similar based on aicraft type. Use Mark 1 human brain, exerience and training. Occasionally with very small loads, add ballast.
3. Bound up the stairs when she arrives and stick your head on the flight deck and say "How much fuel for the loadsheet skip?" Add numbers to loadsheet.
4. Check-in closes. Add pax numbers and bags to loadsheet.
5. Check bags and cargo in the right place.
6. Drop trim line and put a cross where the TOW and LW are.
7. Add LMCs (last minute changes) for the runner that arrived at check-in 10 minutes before departure.
8. Sign and present clipboard to captain.
9. Tear off a copy and exit stage left.
10. Put on headset (or just earplugs) and do startup and pushback.
Now your electronic jobby might look highly accurate but with the lack of skill and different languages at LGW, it has been known for the a/c to depart with the inbound cargo still on board and not on the loadsheet.
And all my manual jobs took to the air and landed safely, so not much must have been wrong.
Electronics (like calculators) give an illusion of accuracy and expertise where none may exists.