Anyway here's list of few things

Weather Bonuses on Gear
Bonus Weather Materia
Weather Bonuses-towards Crystal Elemental (Can we have it for Primal Summoning-Force Weather Change)

DoL & DOH on gear and finding rare items.
Small Damage Bonuses towards right elemental attacks/magic under the right weather.

Special Enemies appear in Weather (more then Dolmore) Can we have Elementals.

This also for Daytime & Night time Enemies. Undead/Bats/Wolfs etc.