Landing fees are per movement, irrespective of how many people are on the flight? They can also offload the cost of the expansion on existing airlines through additional rises in landing and passenger handling fees.
Landing fees are generally based on maximum take of weight/ mass of the aircraft.
Most airports also have a noise multiplier built in to the calculation too.
Passenger fees are obviously per passenger.
Pinching Gatwick Traffic through an expansion (which implies Heathrow was full or close to being so) would make connectivity much better. Putting the xenophobia against foreign ownership aside, like we don't have any investments abroad, it would be saying like merging all the London terminals into a London hbf wouldn't bring connectivity benefits
Gatwick is also planning a big expansion - though it's much cheaper and easier than Heathrow's and entirely privately funded.
I can't see LGW pasenger figures going down to be honest even with Heathrow having a third runway. London passenger growth is very decent and 2025 will likely see all airports above 2019 figures.
2024 figures have Heathrow serving 83.9 million passengers.
Gatwick's final figures aren't out yet, but in 2023 they served just over 40 million and based on summer figures, I'd expect the final number to be around 44 million.
Luton served 16.7 million.
Stansted served 29.8 million.
London City figures aren't out yet - but will probably be in the 4-5ish million range.
Southend served a couple of hundred thousand, though easyjet is opening a base this year.
For Heathrow and Stansted, they are record numbers. Luton served 18.2 million in 2019 and Gatwick 46.6 million in 2019 so are close, but not quite back to pre-Covid numbers.
That's a lot of passengers and very strong growth year-on-year with no sign of that growth abating. There's no reason why a three runway Heathrow serving around 100 million passengers a year would greatly affect the other airports.
The London airports serve such a wide area, it often makes sense to serve multiple airports to the same destination.
Emirates flies to Heathrow, Gatwick and Stansted to/from Dubai.
Ryanair flies to Stansted, Gatwick and Luton to/from Dublin.
BA flies to Heathrow, Gatwick and City to/from Gatwick.
Take Emirates' example. They already fly to Heathrow six times a day. They can afford to buy slots, but think it makes more sense to add capacity to Gatwick (3 daily), and Stansted (twice daily) than fly even more to Heathrow.
Though your point on connectivity is totally right. A better connected UK is better for the UK. Even if it means BA might sell some seats from AMS-LHR-JFK cheaper than LHR-JFK because that's how the market worldwide works.