Mr. Smarty Plants is wondering what kind of weeds you have that require that much weed-eating, and how short you wish to keep them? We often recommend planting grasses/grass-like plants to help control erosion on steep slopes, but many of these are 12 inches tall or more. I am going to suggest two approaches to help solve your problem. The first is to introduce you to our Native Plant Database.
Scroll down to the Combination Search Box. and select Tennessee under State, Grass/grass-like under Habit, and perennial under Duration. Check sun under Light requirement and dry under Soil moisture. Click on the Submit Combination Search button, and you will get a list of 20 native grass/grass-like plants for Tennessee landscapes. Clicking on the scientific name of each plant will bring up its NPIN page which contains a description of the plant, its growth characteristics and requirements, and in most cases images. As you check out each plant, you can note its size and other features to see if they might fit your needs.
You can modify your search by going to the Narrow Your Search Box on the right side of the screen and change Grass/grass-like to Herb under General Appearance, and clicking 0-1 under Height. Clicking on the Narrow your Search Box will bring up a list of 12 flowering plants that you can check out.
The second approach is to share the answers to previously asked questions. We quite often get questions about what to grow on steep slopes. All of these questions are from the southeastern US, so growing conditions will be similar to Tennessee. You will find suggestions for plants in each answer along with images of the plants.
Virginia, talks about not cutting the grass can strengthen the roots