The Weares are a natural formation but the name may have come from some artificial local construction. Above the naval dockyard was a fortification called The Verne which was built to keep out Napoleon. This is also now a prison but many of the words used in fortification are still in use as place names. Glacis for example - so this could explain the use of the word Weare. The following will explain why the formation occurs.

http://www.swgfl.org.uk/jurassic/geoland2.htm

A bit more general info on how the stone was quarried and added to the natural process of forming the Weares.

http://psqt.org.uk/iq/bp.history_quarry.html