I'm just curious, nobody has been able to answer me this at my locals. 

I think G probably means how many beys you can use, like 5G case has 5.

There is no 3G battle, back then it was (and is still) called 3-on-3 battle.
It initially came from 5G, the new format introduced during GT season.
I don't really know what the G stands for, but it might have something to do with GT.
Reference: TT's video introducing 5G battle https://www.youtube.com/watch?v=uiV2N62jTXE
(They mentioned 3on3 on the 45 seconds mark)

Halo KLP

...in video description there is a bit of text that may hint on what "G" stands for, but I may be wrong. It states the following:

"マスターブレーダーたちのガチンコベイバトルが再び勃発！"

which Google roughly translates to: "The Gachinko Bay Battle of Master Braders breaks out again!"

I guess G stands for word "Gachinko" which now means "competing in earnest/serious way". Here's a bit more on the meaning of the word:

https://cotoacademy.com/gachi/

since it's older meanings (“serious match”, “a heated battle”, “a violent collision”) are even better suited to the context of Beyblade battles.

...