Fertilizing once a week means relatively low light, otherwise the plants grow so fast they deplete the nutrients before the next dosage is added. If you add enough to last through the week you really do have a lot of nutrients in the water after you dose. A 48 inch long tank 21 inches in height gets plenty of light from a couple of T5HO 54 watt bulbs, but too much to be fertilizing only once a week. You will need pressurized CO2 also, to maintain a steady, high concentration of CO2 in the water.
If you use ADA Aquasoil you might be able to dose the tank only once a week, because that substrate is rich in nutrients. But, making the substrate provide most of the nutrients, with relatively high light, means the substrate nutrients start to be depleted pretty quickly.
You can have weekly fertilizing, and the slow growth that goes with that, by using lower light intensity, but you can't easily have it with high light intensity. You can always reduce the light intensity by raising the light a few inches.