From the Super Mario Wiki
Tweesters are tornado-like enemies found in many Mario games that try to touch Mario to send him into the air in an attempt to redirect his movements and hinder his progression. In most of the games they cannot harm Mario directly and can only attempt to force him into a more dangerous situation. They are usually found in desert levels.
Super Mario series
Super Mario Bros. 3
In Super Mario Bros. 3, their only appearance was in the Desert level of Desert Hill, where they would trap Mario in an air pocket and move him backwards. The only way to get past one would be to run until the P-Meter's reached P, and then jump into the air before the player hits the Tweester. There is no way for Mario to defeat a Tweester, and so they will always remain in their location.
Super Mario 64/Super Mario 64 DS
In Super Mario 64 and its remake, if Mario touched one of them, he would be sent upwards and slowly float downwards as if he had jumped off a Spindrift. They are also situated next to quicksand, which is a tactical spot for them to be placed so that they can try to get Mario to be defeated. They appeared in Shifting Sand Land.
Super Mario Sunshine
New Super Mario Bros.
In New Super Mario Bros., Tweesters appear in World 6-A. They are very big and immobile, and they no longer have mean faces. If Mario comes in contact with one, he would be sent upwards and do a Spin Jump, similar to in Super Mario 64.
Super Mario Galaxy
Tweesters appear in Super Mario Galaxy; however, instead of having menacing faces, they only have white eyeballs that follow Mario, no mouth, and they are actually a bit helpful. However, the garbage they are flinging around can hurt Mario or Luigi if he makes contact with it. Also when the player touches one, he will spin around. Then he has to do a spin, and the Tweester will make him go flying in the air while Mario or Luigi spins his arms around very quickly like a helicopter. This allows Mario to fly like a helicopter for a very short time. Similar and bigger tornadoes without eyes called Galactic Tornadoes also appear in this game. These tornadoes appeared in the Dusty Dune Galaxy and made a small appearance in Bowser's Galaxy Reactor. Tweesters do not appear in the sequel, Super Mario Galaxy 2.
The Adventures of Super Mario Bros. 3
In Paper Mario, the first game where they had menacing faces, they would blow Mario one screen north and one screen east in Dry Dry Desert. It is highly recommended not to touch them, as Mario could easily get lost in the vast sands. However, one particular Tweester (in an area with blue cacti) could blow Mario near a Badge on top of a high rock, and this Badge could not be reached by any other means.
Mario Party series
Like many other minor enemies, Tweesters were featured as Capsules in the Mario Party franchise. In Mario Party 5, a Tweester Capsule would send the Star to a new location, echoing the roles of the Lucky Lamp in Mario Party 3 and the Chomp Call in Mario Party 4.
In Mario Party 7, they took the player to another place if they walked over one of them.
Dance Dance Revolution: Mario Mix
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