Did you know…
How much do airports charge for excess baggage?
Short answer
Airports don't charge passengers for excess baggage: that fee is set and collected by the airline, not the airport operator. Airports do bill airlines separate fees for landing, parking and terminal use, calculated by the aircraft's maximum takeoff weight or per boarded passenger, not by individual baggage.

It's common to confuse two different things: the excess baggage surcharge, which the passenger pays to the airline, and airport fees, which the airline pays to the airport operator for every flight it operates.
Who actually charges for excess baggage
The charge for an extra bag or extra kilos is set by each airline within its own conditions of carriage, and it's billed directly to the passenger, usually at check-in at the airport or, more cheaply, by purchasing it online in advance. The airport operator has no part in that transaction and receives none of that revenue: it's a purely commercial surcharge from the airline, not a public fee.
What fees airports do charge
Airport operators — in Spain, mainly Aena — charge airlines fees for landing and takeoff, for the time the aircraft spends parked on the apron, for the use of boarding bridges and check-in counters, and a per-passenger fee that helps fund terminal upkeep and security services. These fees are calculated based on the aircraft's certified maximum takeoff weight (MTOW) and the number of passengers it carries, not on how much baggage each individual passenger brings.
Where the confusion comes from
Since the cost of excess baggage often appears alongside other fees and surcharges during the ticket-purchase process, it's easy to mistakenly attribute it to the airport. But except for very specific cases involving airport ground-handling of checked baggage, the airport neither sets nor collects that charge.
More questions

Foto: 4300streetcar (CC BY 4.0) Commercial aviation
Which 747 carried Enterprise "piggyback"?
The first Shuttle Carrier Aircraft was a Boeing 747-123 registered N905NA, originally built for American Airlines and acquired by NASA in 1974. Boeing… more…

Commercial aviation
Was there an amphibious DC-3?
Yes: the Douglas XC-47C was created by fitting Edo Model 78 floats onto a standard C-47. The single-step metal floats carried retractable wheels that also… more…
_Berliner_Luftbr%C3%BCcke.jpg)
OTFW, Berlin (CC BY SA), vía commons Commercial aviation
Was a C-47 converted into a glider?
Yes: the Douglas XCG-17 was an assault glider created by converting a twin-engine C-47 Skytrain during World War II. Its engines were removed and the nacelles… more…

Commercial aviation
What did the USSR build from the DC-3?
The USSR built a version of the DC-3 under a licence granted to its government on 15 July 1936. It was designated PS-84 and, in 1942, renamed Lisunov Li-2… more…

Commercial aviation
What was "Puff, the Magic Dragon"?
It was the nickname of the Douglas AC-47 Spooky, the first in a series of fixed-wing gunships developed by the United States Air Force during the Vietnam War… more…

Commercial aviation
How did the RAF refer to the C-47?
The RAF called it Dakota: the Dakota I was the designation for 53 C-47s received under Lend-Lease. The Dakota III designated 962 C-47A Skytrains. The Dakota… more…