Certified GKH Gardening Expert
Sounds like the beets may not be mature or ready for harvest. They can be grown throughout fall/winter in warmer areas. You may need to allow more time to pass and then check the plants again to see if they have reached the desired size. The following article may be of some help: https://www.gardeningknowhow.com/edible/vegetables/beets/growing-beets.htm
Additionally, adding some phosphorus-rich fertilizer will help with root development.