Strengthening Weapon

How would I add a custom weapon that treated the character as having a strength 1 die size larger for determining damage? So, for a melee weapon doing d6 damage wielded by a d8 Strength character, it would do d10+d6 instead of d8+d6? I see that I can add a weapon that just does d10+d6, but I'd like a general weapon that I could assign to characters and have it behave appropriately without needing to manually change for each character.

d6+Str! Would do that. Exclamation mark after Attribute in weapon damage means increase the attribute by one die type.

d6+Str!! Would increase strength die type by two.

That's it. Thank you.

OK, so since that one was so easy, is it possible to add a die to a roll in an Effect instead of a static number? For instance, if I wanted to have an effect that added +d4 Melee Damage.