Musculoskeletal strain or sprain: Given the acute onset of back pain and bilateral leg weakness without significant laboratory findings (negative ESR, CRP, and MRI lumbar), a musculoskeletal issue such as a strain or sprain is a plausible explanation. These conditions can cause significant pain and weakness, especially if the muscles or ligaments in the lower back are affected.

Lumbar disc herniation: Although the MRI lumbar is reported as negative, it's essential to consider that some herniations might not be visible on MRI, especially if they are small or if the MRI was not of high quality. Symptoms can include back pain radiating to the legs, which might be perceived as weakness.
Peripheral neuropathy: Conditions affecting the peripheral nerves, such as Guillain-Barré syndrome, could present with weakness. However, the absence of fever and negative inflammatory markers makes this less likely, but it cannot be ruled out without further investigation.
Spinal stenosis: This condition can cause neurogenic claudication, leading to leg weakness and pain, especially after walking or standing. It might not always show up clearly on an MRI, especially if it's a dynamic condition.

Spinal epidural abscess: Despite the negative ESR and CRP, which are markers of inflammation, a spinal epidural abscess is a medical emergency that requires prompt diagnosis and treatment. It can present with back pain, fever (though the fever might be absent in some cases), and neurological deficits such as weakness. The absence of fever and normal inflammatory markers does not rule out this condition.
Cauda equina syndrome: This is another emergency that requires immediate attention. It can result from a variety of causes, including a large disc herniation, and presents with low back pain, bilateral leg weakness, and potentially bladder and bowel dysfunction.
Infectious discitis or osteomyelitis: These infections can cause back pain, fever, and neurological symptoms. The fact that ESR and CRP are negative does not exclude these diagnoses, as some cases might have a more indolent onset or the markers might not be elevated early in the disease.

Neurosyphilis: A rare condition that can cause a wide range of neurological symptoms, including weakness and back pain. It's less likely but should be considered in patients with risk factors for syphilis.
Sarcoidosis: This autoimmune condition can affect various parts of the body, including the nervous system, and might present with back pain and neurological deficits. However, it's relatively rare and usually has other systemic symptoms.
Vitamin deficiencies (e.g., Vitamin B12 deficiency): Can cause neurological symptoms, including weakness, but would typically have other associated findings such as sensory deficits or changes in reflexes.