in current English gran is an acceptable short form of grandmother/grannie etc.
Is this where the English term gaga comes from, via the French gaga - senile person?
I'm not completely sure but I think the word "γιαγιά" might come from the Catalan "iaia" (pronounced as yaya) which translates to grandmother. Personally, I think the pronunciation sounds a bit closer to it than "gaga" does ^.^
The etymology of the greek word (as far as I know and in every etymological dictionary I looked into) is sound-mimicing of the sounds that babies make. It may be the same for Catalans and the words are possibly not related.
I said it because it was funny seeing that it's the same I call my grandmother, written yaya in Spanish. I looked it up before checking the comments and found some forums where they said that it came from Greek (via the Mediterranean, and then to America, where it's used in many countries), although the official dictionary says its origin is uncertain. I suppose we'll never know, but even if many languages have come to similar words independtly, I see some relation between the two, been so close (remember that the Catalan Company conquered the duchies of Neopatras and Athens and imposed the catalan as official language, even if not for a long time...).
In fact it makes sense that the catalans that moved there during the occupation had left some words behind...
As I said, not sure about that. :/ I do remember that a philologist of mine in Highschool told us so, in class. I searched it up a bit and found a couple of sites that do agree with it. Everything is possible when it comes to etymology though :p
In catalan we have yaya for grandmother and yayo (iaiou) for grandfather. It's an everyday word. The most formal word is avi (grandfather) and avia (grandmother).
The almogavars were mercenaries in the Middle Ages who came from Catalunya and other parts of Aragon. In a certain point they were hired by Greece and they left some words in their vocabulary. One of them is yaya. @Perriguez is right.
Btw,there is an article in Wikipedia if you are interested about the almogavars. :-)