I have iced 4 tiers today. I had perfectly smooth edges with butter cream chilled it and covered in static ice. It looks smooth and perfect. 4 hours later the sides have a slight dived effect where you can see the layers! How do I stop this? Is my fondant too thin? I rolled to about 4-5mm. Is the fondant too heavy?

It sounds like your layers are settling and the filling is being pushed out the sides. You might want to try using cake spackle on your cake before covering it with fondant. It's basically cake scraps mixed with enough frosting to make it spreadable. You can search CC or Google for the technique. My cakes look much smoother since I've started doing this.