Why does the mercury amalgam fillings cause my teeth to be dark underneath?

Corrosion: Amalgam fillings are metal and the longer a metal stays in a wet environment the more likely it will corrode. It's that corrosion that will cause the tooth to appear to darken. It's also the corrosion that will eventually cause the filling to need to be replaced.

Corrosion: Some amalgam fillings can corrode over time and the byproducts can be absorbed by the neighboring tooth structure. While not cosmetically pleasing it is harmless to your tooth. The mercury is chemically bound up and is not being released. If you are concerned about cosmetics see your dentist about your options for a more cosmetic replacement. Otherwise leave them alone.