A Weather Report was a forecast of the weather.
In 2151, while dealing with an away team stranded on the planet that would later become known as Archer IV, Jonathan Archer requested a weather report. (ENT: "Strange New World")
In an alternate reality, one of the news feeds on admiral Alexander Marcus' wall display showed a 2 News Earth Sector 2 news report. (Star Trek Into Darkness, production art)
In 2374, B'Elanna Torres complained that Vorik delivered a particularly dire engineering assessment as if it was a weather report. (VOY: "Demon")