In the main series games, there are items that effect the weather, but don't change it.
These items include the Heat, Damp, Smooth, and Icy rocks, which make Sunlight, Rain, Sandstorm, and Hail last for a few more turns than normal. There are also the Safety Goggles which makes you immune to powder and damage from Sandstorm and Hail, and the Utility Umbrella, which negates the effects of Rain and Harsh Sunlight.
However, in side games like Mystery Dungeon, there are items that can change weather.
In Mystery Dungeon, there exist items that have an effect on weather and can change weather. Sunny Orb changes weather to Sunny, Rainy Orb changes weather to Rain, Sandy Orb changes weather to Sandstorm, Hail Orb changes weather to Hail, and Weather Lock Orb which changes weather to clear and prevents it from being changed for a while. There are also items that allow you to avoid damage from weather like Weather Band and Weather Looplet.
Source: This, parts of this, and experience. Hope this helps :)