Similar to you, for a private project in the past I wanted some statistics about airports and came across the hurdle that to access such information was too expensive for an individual.
In the end the best sources I could find where either;
- National transport authorities of various countries (such as the FAA,
The national transport authorities have varying amounts of statistics, and suffer from the problem that some publish data, some don't publish in English, some don't publish at all and of course that you need to search 100s of authorities to try to get all the data!
(PS. You can try Eurostat for the EU).
So realistically this is only possible for a few of the authorities.
Wikipedia.org is another source. Generally they only publish data on specific themes such as "busiest airports by passenger traffic" (https://en.wikipedia.org/wiki/List_of_busiest_airports_by_passenger_traffic).
Of course, it might not be as accurate, might be out of date. But you can also see links to the sources used, which might also help.
Often you can find sub-sections (not always linked so you have to search via google), so that you might be able to also find out similar details for each Continent, geographical region, and sometimes countries.
For example: If you looked at "Busiest airports by continent"
then you have an expanded list.
Plus, at the bottom of the page are sublinks to
Then sometimes when you look at these, you find other links. E.g. If you looked for Europe then there also links to UK, Germany, Spain etc.
In the end, these were the best sources that I could find for free.
If you are doing your research as part of studies for a university degree or similar, then I would additionally suggest that you try to reach out directly to IATA, ACI (Airports Council International) and see if they might provide you with a limited dataset (maybe 1 or 2 years out of date) which you might be able to use for free.