Does water/Air/Darkness/ earth based weapon have any special advantage like the armour and ring. Does..

Only the Light based weapons have the notable exception of being able to pass Light barriers. Other elements on weapons may contribute to resistance/vulnerability of enemies, but are not as noticeable. At later levels sufficiently upgraded weapons of an element may also confer immunity as if it were an armor piece of the same element.

Light barriers can be passed without needing to equip Light armor/ring.