"airport system" implies a single ownership / management often part of city government - e.g. Port Authority operate LGA, EWR & JFK.
I believe there is a body which declares whether an airport is part of a city or not - I know they recently declared Niederrhein a Dusseldorf airport, even though the FR website has it as Niederrhein-Dusseldorf, not under D for Dusseldorf.
I tend to use OAG to determine if an airport comes under a city or not, and would include both BGY and PIK under their respective cities.
Another argument would be to do it be mileage - say 100km, although this would then bring CVT under BHX, and both GLA and PIK under EDI (sorry, had to get that one in, sure it will provoke a few people
).
Interesting to see how close DUB & AMS are to each other, I presume they are the top 2? Is PAR 3?
Also, if you add LHR+LGW+STN+LTN+LCY, I think that makes London the clear aviation capital of the world - over 100m, with Tokyo or Chicago #2? Despite all the talk of AMS, CDG or FRA catching up with LHR for transit traffic, they are all quite a few million paxpa behind.