Chronic Venous Insufficiency (CVI): Given the patient's significant family history of varicose veins, the worsening of symptoms throughout the day, and improvement with elevation, CVI is a highly plausible diagnosis. The patient's symptoms of bilateral leg swelling, skin color changes, and low back pain are consistent with this condition.

Varicose Veins: Similar to CVI, varicose veins could explain the patient's symptoms, especially given the family history. The presence of varicose veins could lead to venous insufficiency, causing the described symptoms.
Deep Vein Thrombosis (DVT): Although the patient denies recent long travel or history of circulatory problems, DVT should be considered, especially if there's any possibility of undiagnosed thrombophilia or other risk factors not immediately apparent.
Lymphedema: This condition could cause leg swelling, but the absence of other typical symptoms like heaviness or tightness in the skin makes it less likely. However, it remains a consideration, especially if other diagnoses are ruled out.

Abdominal Aortic Aneurysm (AAA): Although less likely given the patient's age and lack of abdominal symptoms, AAA could potentially cause low back pain and leg symptoms due to compression or embolism. It's crucial to consider this diagnosis due to its high mortality rate if ruptured.
Spinal Stenosis or Disc Herniation: These conditions could cause low back pain and potentially contribute to or mimic leg swelling symptoms if there's associated neurological compromise affecting venous return.
Malignancy (e.g., lymphoma, abdominal or pelvic tumors): Tumors could cause obstruction of venous or lymphatic return, leading to swelling. Given the gradual worsening of symptoms, malignancy, although unlikely, must be considered to avoid missing a potentially life-threatening condition.

Klippel-Trenaunay Syndrome: A rare congenital condition characterized by varicose veins, hypertrophy of the affected limb, and sometimes lymphatic abnormalities. Given the family history of varicose veins, this could be a consideration, although it's much less common.
May-Thurner Syndrome: A rare condition where compression of the left common iliac vein by the right common iliac artery leads to DVT or chronic venous insufficiency. It's an uncommon cause of leg swelling but should be considered in the differential diagnosis, especially if other causes are ruled out.