They've been expanding their airports over those 20 years; Barcelona's passenger air arrivals has doubled in that time and there is another expansion being planned. Barcelona is not a large city and they should really be coupling every airport capacity increase with an equal increase in tourist accommodations or they end up in an even worse situation.
Spain's airports are quite interesting. They're all owned by a monopoly which sets the same landing fee to land at any airport. So high volume airports are effectively cross subsiding building very good airports in the smaller regional areas.
Not great for prices (Ryanair is complaining about high landing fees) but it does mean tourists have a good job being dispersed into the countryside and having a good experience.
By what measure? Granted, I now live outside of Barcelona after moving here from an island with ~700 people on it, so for me pretty much any city is big, but I'm fairly sure Barcelona is within top 100 worldwide in terms of population living in it, so I'm guessing you're saying "not a large city" by some other metric?