Uotchi is the Japanese word for watch. Tamago (egg) and Uotchi (watch) - so here they're implying "Weather Watch", it should probably be Weatherotchi or something, but still works fine imo. Korea and Japan love smashing words together to make new words, for example in Korea "Chimaek" is Chikin (치킨 - fried chicken) + Maekju (맥주 - beer), something Koreans often ask if you'd like to go out for.