Well, it has a reasoning when it comes to naming/coding aiports.
    Let´s see for example, Teresina.

http://www.world-airport-codes.com/alphabetical/airport-code/t.html
   Couldn´t be TER, for example, if you would put TER as the Teresina airport, the code would double with the one of the city of Lajes Ab in Portugal. So, no way José!

    What about inverting the letters, TER is the code for Tiree airport in the United Kingdom, so the trigram was already "occupied".

    TRS already is used for Ronchi Dei Legionary in Italy, TRN is another use for an airport in Italy.
   TRA is one code for an airport in Japan, TRI in the United States, TRO in Australia,     TRU in Peru.      All initiated in TR* used then.
        So, the only letter it could be chosen there was the T, the initial for the city, the rest was taken at the time of the choosing.
        On the other hand, the airport of Teixeira de Freitas was luckier, it got the TXF tree-letter acronym!
      You can see that Matei (no, I didn´t killed anybody - it´s the name of the airport in Fiji !) couldn´t choose even the initial, it is TVU!
     When it comes to aiports coding, he who comes early takes the worm!
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On the BS trigrams, we can see that:
    Bossaro, Somalia (BSA)
    Brasilia, DF, Brazil (BSB) Indeed Brasilia was lucky by having the letters BS (certainly taken from Brasilia) and B likely from Brazil. But it may had have the
option of choosing it at the time...or maybe another factor in play, maybe we never will know.

     Bahia Solano, Colombia (BSC)
     Baoshan, China (BSD)
    There is no BS-E/F/G/H/I/J, for that matter.
    Biskra, Algeria (BSK)
    Basel, Switzerland (BSL)
    Basco, Philippines (BSO)

http://www.skygod.com/asstd/abc.html
A good site for the explanation of the dynamics of coding aiports, you will know
how some aiports got that strange (at first) trigram.
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Maybe these sites can be useful to the more curious, it will be placed just as a plus (courtesy here).
http://www.logisticadescomplicada.com/pesquisa-infraestrutura-aeroportos-brasileiros/
No Brasil são usados os seguintes códigos ICAO: SB,SD,SN,SS,SW
http://www.postmodern.com/~mcb/misc/code.html
You can see IATA 3 letter and ICAO 4 letter code here.
BSB Brasilia, DF [Internacional],
Brazil SBBR Brasilia Aeroporto Brazil

THE Teresina, PI, Brazil
SBTE Teresina Aeroporto Brazil
http://www.mapping.com/airportcodes.shtml
ICAO CODE
SBTE
SBXE
FAA or IATA CODE
THE Teresina PI [Teresina]

http://www.meioaereo.com/index.php?option=com_content&view=article&id=418:codigos-de-aeroportos-brasileiros-iataoaci&catid=83:aeroportos&Itemid=459

Certainly if the "Aeroporto Intl. Prefeito Dr. João Silva Filho - SBPB - (In Parnaiba) had been the same as "Aeroporto Intl. Presidente Castro Pinto " - SBJP - because of the state it would make confusion.
You would say "but it would be only to invert to SBBP, no way, it has an such code to the airport of Bragança Paulista - SBBP.

Well, you have that inversion in Rio, okay, since if you misunderstand the code and it is going to the wrong place, at least it is not that far away, you would only spend some extra aviation fuel!

http://www.oragoo.net/quais-sao-as-siglas-dos-aeroportos-brasileiros/