a generation of kids weaned on television [=a generation of kids who have watched television a lot since they were very young]从小就有看电视习惯的一代孩子

Although born in the 1970s, the singer says she was weaned on the music of the 1940s.虽然生于20世纪70年代，但这位歌手说她从小就熟悉40年代的音乐。