More and more people choose to wear the sunglasses not only for the avoid of UV but also for the coolness or beauty. These two aspects should be cared when you pick the sunglasses: its function and appearance. About whether you should wear the sunglasses covering your eyebrows, it depends on your using habit. There is no relation with the eye health. If you think it looks cool, you can just wear in this way.
Well, this is your personal favor. As you like big framed sunglasses, you can have one cover your eyebrows. But there is something you can take into consideration. If your face or head is not big, you'd better not wear too over-sized sunglasses as they may cover almost all your face. It's wired, right?
Really, it varies from pair to pair, and depending on where you go, because the associate will help you pick out the right ones for you. Personally, I think it does not matter because when i buy the sunglasses, I will take into the shape of my face and the sunglasses consideration. Nevertheless, some certain style will cover your eyebrows, as some large pairs look really cute and cool, but others just make you look like a Fly Lady. Use your own judgment.
It all depends on your own needs. Because whether the sunglasses cover your eyebrows or not, it will not do any harm to your eyes' health. As we know that there are more and more people who choose a pair of sunglasses to make them look cool and nice but not just for UV protection. In your situation, you also can choose a pair of sunglasses which can cover your eyebrows and protect your eyes from the sunshine. But you should also know that no matter which style you will choose, you may choose ones that fit you.