Allergic Rhinitis or Sinusitis: This condition often leads to increased blood flow and congestion in the nasal passages and surrounding areas, including under the eyes, causing a red or purple discoloration due to the thin skin in this area.

Fatigue or Lack of Sleep: Prolonged lack of sleep can cause increased blood flow and puffiness under the eyes, leading to a darker appearance.
Dehydration: Inadequate hydration can lead to a decrease in skin elasticity and an increase in the appearance of blood vessels under the eyes, making them appear more red or purple.
Aging: As people age, the skin under the eyes becomes thinner, and fat pads can shift, making blood vessels more visible and causing discoloration.
Genetics: Some individuals may naturally have a more pronounced appearance of blood vessels under their eyes due to their genetic makeup.

Basal Cell Carcinoma or Other Skin Cancers: Although rare, skin cancers can present with pigmentation changes, including red or purple discoloration under the eyes.
Thyroid Eye Disease: Associated with Graves' disease, this condition can cause bulging eyes, redness, and swelling, including under the eye area.
Vitamin Deficiencies (e.g., Vitamin K or B12 deficiency): Certain vitamin deficiencies can lead to easy bruising or changes in skin pigmentation, which might be noticeable under the eyes.

Amyloidosis: A condition characterized by the deposition of amyloid proteins in various tissues, which can lead to skin discoloration, including under the eyes.
Sjögren's Syndrome: An autoimmune disorder that can cause dry eyes and potentially lead to discoloration under the eyes due to chronic inflammation.
Methemoglobinemia: A disorder that affects the hemoglobin in red blood cells, leading to an abnormal amount of methemoglobin, which can cause the skin to appear blue or purple, including under the eyes.