I've just started playing Legion as the Empire and last weekend I ran into the following.

While attacking with Boba Fett I wanted to use his Arsenal 2 ability to attack a rebel unit that was at within range three. This is where the disagreement with my opponent started.

My opinion is the following:
The Arsenal keyword states that: "To use a weapon during an attack, the defender must be at or within any of the weapon's ranges". Being that the unit was within range three it, met the condition for Arsenal and I could combine the dice pool of the EE-3 Carbine and the wrist rocket. (i.e. the key word states any weapon, not all weapons).

My opponent didn't agree:
When using Arsenal, the dice of different weapons can only be combined if the target/targets are within the range of both weapons.

I think the disagreement stems from the fact that we are both non-native English speakers and maybe something gets lost in translation. How do you interpret this rule, or what is the official ruling?

You have to check for range on any weapon you want to fire. So at range 3 you can only shoot one weapon. You could shoot on a different target within range 2 with the second weapon though.

As @SailorMeni said, in that case you can only use the weapon that has range 3.

That is because you are making an attack, so you don't have to take into account only the rules for Arsenal X but for attack too:

b. Choose Weapons: The attacker can choose one weapon from each eligible mini to contribute to the attack pool. To choose a weapon, the attacker must meet all requirements indicated by that weapon’s keywords, and that weapon’s range must include the range of the attack, as determined from the attacker’s unit leader to the closest mini of the defender.