What causes puffy eyelids?

Many factors. I am assuming you mean lower eyelid puffiness? There are many factors to contribute to this- lack of sleep, high salt diet, allergies, and most commonly hereditary anatomy. It is usually the lower eyelid muscle and soft tissue layer loosening over time, allowing the fatty tissue behind it to bulge outward. Surgery can help reduce that, but it will not affect the other factors i mentioned.
Many reasons. There are many reasons for having puffy eyes: heredity, allergies, too much salt, eye disease, systemic diseases; these are a few.
Many causes. Eyelid swelling can be caused by many things. See an ophthalmologist for evaluation if you want this to better.

Related Questions

Does blepharitis cause puffy eyelids?

Possibly. Blepharitis is an infection of the eyelashes. Usually it is localized to one eyelid. If both eyes are puffy another cause is more likely. Read more...
Yes. Yes. Blepharitis is caused by blocked up oil glands which lead to inflammation. Inflammation lead to bleed vessel dilation, fluid accumulation, and secondary puffiness. Read more...

I am having symptoms similar to hyperthyroid. Could overmedication also cause symptoms of graves disease particularily the puffy eyelids?

No. Once diagnosed with any thyroid condition, the condition known as "thyroid eye disease" can occur at any time, independent of the thyroid status of the body. So in your case, the puffy eyelids is due to the thyroid condition, not the over-treating or under-treating of the thyroid in the body. Read more...