From the wiki we know that Weapons have a weight and that does affect the movement ability during skills.
Now there are many different types of weapons some being 2 handed others being one handed, some allow dual wield.
The dmg listed on the weapons will affect the damage of skills. from a other game that also had dual wield as well as single and 2 hand weapons it had a system to it that:
2 handed weapons could be fused together in order to compensated the 2 hands needed while one handed weapons had the effect that the main han dmg counted 100% while the offhand dmg only added 50% to the total dmg. and since it also had shields it could provide additional defense for the missing dmg from the offhand.
how exactly the math behind the damage calcs in Aoc will be i don't know.
but
What if weapons also bring additional effects to the skills like:
cast time enhance or reduction, cd enhance or reduction, dmg enhance or reduction, compensation instead of crit
here some example what that could mean:
The Tome is 2 handed it does enlarge the cast time but thru that also enlarges the skill dmg
meanwhile
Wands reducing the cast time (or even reaching instant level) but reducing the dmg
Also the Tome does do cirt hit in dmg while wands compensate posible crits in skill cd reduction
same effects for melee weaponry
Shields enlarge the defense but may also enlarge the healamount of healing skills.
Skills that have a cast time to it could also cast as long the player keeps holding the skill button pressed and release upon stopping to hold so the skill charges up and becomes stronger however without a bar or so displayed so it comes to player knowledge when the best time is to release, when the max possible damage output is reached. Also could cast time also affect the manacost of a skill.
Much like chargeable skills
for weapons
2 handed be:
Bows, Crossbows, Grand Sword, Battle Axe, War Hammer, Pike, Halberd, Spear, Staff, Tome
while singlehanded be:
Mini Crossbows, Shuriken, Sword, Dagger, Rapier, Axe, Mace, Mallet, Wand
just a funny mention:
even if it would be funny but i don't recommend to add is dual wield wands (the pew pew laser wands) or dual wield shields especially if the crit brings cd and the cast time is reduced by the wielding of wands or becoming a healing turtle but without many options to do dmg

Have a happy day
Asraiel