Why does the Aburame clan cover their eyes?
They do not cover their eyes. They use sunglasses/dim glasses for protection. 

Since they are known for having the characteristics of insects, we can assume that they have crepuscular vision and some have nocturnal traits - meaning that they are most active in twilight/low light/night. Their eyes are highly adapted on low light.

Therefore, using their naked eyes are like humans using Night Vision goggles. Just imagine the amount of light they will receive during daylight.

Source: Insect Vision