You and your cousin are not gonna have flipper babies, but after doing this for several generations, your descendants will all have PCOS and astigmatism, they will need glasses for poor eye sight, and probably several of them will be physically and mentally disabled. There is a lot of research to back this up, and if you don't believe in research, you can compare the side of your family that have been inbreeding with the side that have not and you can see for yourself.

Edit:

I'm gonna add that if you are considering marrying your first cousin, you undoubtedly already have family members that have been marrying eachother for several generations and you probably also personally know several people with some or all of the issues highlighted above, which is all the more reason for your family, friends and wider society to bully you out of doing it again yourself.

Also relevant Dead South song.