What can cause severe lower back pain and leg weakness?

Could be referred . Low back pain with radiation down one side of the leg could be due to a pinched nerve. If you injured your back, strained muscles of the back and hip can irritate a nerve or cause a herniated disc which pinches the nerve. Fortunately this can be resolved non-operatively in most cases. Moist heat, light stretching and over the counter anti-inflammatory medications may help. Persists? See you doctor.