True, the man should do the shopping. That gives the woman enough time to clean the kitchen in preparation of cooking whatever he brings back.
Just think of it like I do: Tetris with groceries. Even hum the theme/make turning noises in your head to get yourself started.
Although the "heavy at the bottom/light at the top" method is simply common sense, it's surprising how many people don't follow this and wonder why their Kingsmill is flatter after the drive home. Nothing to do with the jumbo box of Persil on it, oh no.