In the overworld, you will find that the world is being scorched by sunlight in Omega Ruby, or flooded by torrential rainfall in Alpha Sapphire, both to the awe of the various people witnessing it.
According to the leader of the other team, Kyogre/Groudon will be heading for the Cave of Origin near Sootopolis where it will be able to then use Primal Reversion, unlock its true power which is many times worse than this.
Steven will then come down to you, apologizing for the delay before speeding along to Sootopolis; there, we will get some answers.
New Weather Effects
For all aboveground battles for a while, the weather will be significantly different. For some at least, this will have drastic consequences on the battles between here and Sootopolis and wild battles within the confines of the latter.
Also note that this weather cannot be overridden by any means; for example, the ability Drizzle will not affect the sunlight on Omega Ruby, nor will the move Rain Dance. Similarly, Sandstorm and Hail cannot be induced by any means.
We’re pretty sure even getting one of the Primal Pokémon out in battle - the one of the opposite version - won’t even affect it for plot-based reasons, but cannot be sure as, mechanically, it should. The same would possibly be true for the use of Mega Rayquaza and its Strong Winds.
Note that the ability Cloud Nine will let you ignore the negation effects of the weather.