Muscle Strain: Given the patient's obesity and complaint of pressure and tightness in the muscles at the back of the neck, especially with movement or lifting, muscle strain is the most plausible diagnosis. The strain could be due to overuse or poor posture, common in obese individuals due to altered biomechanics.

Cervical Spondylosis: This condition, involving wear and tear on the discs in the neck, can cause pain and stiffness, especially in the morning or with certain movements. Although it's more common in older adults, the patient's obesity could accelerate wear and tear.
Poor Posture: Obesity can lead to a forward head posture, putting strain on the neck muscles and leading to pain and tightness.
Stress and Tension: Stress can cause muscle tension, leading to pain and pressure in the neck, especially in the absence of other underlying conditions.

Meningitis: Although less likely, meningitis is a potentially deadly condition that can cause neck stiffness and pain, especially if accompanied by fever, headache, and confusion.
Cervical Disc Herniation: A herniated disc can cause severe neck pain, especially if it compresses a nerve root, leading to radiculopathy. It's crucial to identify this condition to prevent long-term neurological damage.
Spinal Epidural Abscess: A rare but serious condition that can cause neck pain, fever, and neurological deficits. Prompt diagnosis and treatment are essential to prevent severe consequences.

Polymyalgia Rheumatica (PMR): An inflammatory condition that can cause muscle pain and stiffness, typically in the neck, shoulders, and hips. It's less common in younger individuals but should be considered in the differential diagnosis.
Fibromyalgia: A chronic condition characterized by widespread muscle pain, fatigue, and tender points. While it could explain the patient's symptoms, it's a diagnosis of exclusion after ruling out other causes.
Rheumatoid Arthritis: Although primarily affecting the hands and feet, rheumatoid arthritis can also cause neck pain and stiffness due to cervical spine involvement. It's less likely in this scenario but should be considered if other symptoms or signs of arthritis are present.