The DRAE (Spanish Real Academy Dictionary) says:
belga Del lat. Belga.
1. adj. Natural de Bélgica, país de Europa. U. t. c. s.
2. adj. Perteneciente o relativo a Bélgica o a los belgas.
bélgico, ca Del lat. Belgĭcus.
1. adj. p. us. Perteneciente o relativo a Bélgica o a los belgas.
So, belga is the usual word, it is the one you should use.
While bélgico, ca is a rarely used word (it is marked as 'adj. p. us' by the dictionary itself, which means 'adjetivo poco usado', little-used adjective). They have almost the same meaning, but you should express nationality only with the first one.
The reason why belga ends with a is etymological, and it’s a word that doesn’t change. On the other hand, bélgico, bélgica uses the normal gender morpheme -o for masculine and -a for feminine.
You say: El belga. La belga. El avión belga. La revista belga.
El avión bélgico. La revista bélgica.
I insist, the second form is rarely used. I myself - Spanish is my mother tongue - didn’t know it exists before reading your question, and it sounds ugly to me.