FFXIII, PSN and Xbox360 9/3/2010

[Pjai]

wats the best way to upgrade weapons?

[Skullator]

I'm not sure of the name of the item in the english version, but you can buy 31 of this item in a shop~
"Perfect jelly" or "Super Jelly" it was called in Japanese version, applying 31 of these to your weapon \ acc. of choice will trigger the triple exp multiplier every time (and 31 of the jelly item is pretty cheap)

After that you pretty much want to use as much expensive \ high exp lvling items as you can at once, it won't stay 3x multiplier for more than one go, so make it a big spend to get the most exp from your gil spent.
You can buy all the best exp items from the shops at save points (They unlock as the game progresses)