A weather satellite was a specialized artificial satellite dedicated to weather monitoring and meteorology.
Nimbus 1 was a weather satellite launched by NASA in the mid-20th century. (TOS: "The Cage")
An "old-style" weather satellite was in orbit below the USS Enterprise when the ship orbited Earth in 1968. Montgomery Scott was able to "bounce off it"" to "get some good views" of McKinley Rocket Base. (TOS: "Assignment: Earth")
A weather satellite was used to monitor the bizarre and dangerous weather on Sherbal V. In 2381, Nick Locarno, or one of the lower deckers he had talked into mutinying against their commanding officers, disabled the satellite's communications relay to prevent people from discovering the starship crews they had marooned on the planet after stealing their ships. The USS Cerritos, unaware of Locarno's activities in the system, sent an away team consisting of Lieutenants jg Beckett Mariner, Brad Boimler, D'Vana Tendi, and T'Lyn on Death Valley to repair the satellite. Once the satellite was repaired, the IKS Che'Ta', patrolling the Sherbal system in search of intruders, attacked and destroyed Death Valley, forcing the away team to beam onto the planet. (LD: "The Inner Fight")