Puffy eyes,also known as the bags under the eyes, can be cause by many reasons. Yeah, as you said, you stay up late recently, so the puffy eyes had a date with you. If you do not want to do nothing with the puffy eyes, you can just leave them alone and have enough sleep, some days later, your puffy eyes will disappointed. Of course, if you want to avoid it through vitamin supplements, you can also finish it. As usual, vitamin C plays an important role in the production of collagen,which is responsible for the structure of cells, then collagen can help you maintain the firmness of the cells under your eyes, which will help you with the puffy eyes. Besides, vitamin E, like vitamin C, can help you keep the strength of your muscle around your eyes. Also, the vitamin E acts as an antioxidant in our body so that they can remove the potentially harmful byproducts of metabolism. Hope you can get helpful suggestion from my answers.