A 62-year-old woman from Delhi presents with a 3-year history of progressive pain and stiffness in both knees, worse in the morning and after prolonged sitting. She has a BMI of 28 kg/m². On examination, there is crepitus on knee flexion-extension, mild swelling, and reduced range of motion. X-ray of both knees shows joint space narrowing, osteophytes at the joint margins, and subchondral sclerosis. She denies any history of trauma or inflammatory arthritis. What is the most likely diagnosis?