AF-C mode is a continuous focus mode. That is, it will not "lock" focus and hold it until the picture is taken. It is best used for when you are tracking a moving subject such as an athlete moving across a field. It will constantly check the focus as the scene changes and adjust to those changes.

The reason you see this behavior even in static scenes is that the NEX-6 uses a contrast detection AF system. Unlike a phase detection system that measures how far and in which direction the lens is out of focus and then moves the lens the (hopefully) correct amount, contrast detection focuses by moving until finding the focus distance that provides the most contrast in a scene. Even when the lens is focused on a static object in AF-C mode, the camera is asking itself, "Is there another focus distance that will provide even more contrast?" I would imagine that the firmware specifies how long to hold that point when it finds it before trying again when in AF-C mode.

In less than ideal light your NEX-6 with a narrow aperture lens will tend to hunt when focus on a subject has been lost. One reason you've noticed it with your 18-200mm f/3.5-6.3 lens is that the smaller aperture allows less light through the lens to be used by the AF system than your 24mm f/1.8, especially at the longer focal lengths of the lens. This is generally one of the weaknesses of high ratio zoom lenses like an 18-200mm. Most higher end zooms only have a zoom ratio of 3x-4x to allow for wider, constant apertures.

If you want the lens to "lock" onto your static subject once it has achieved focus, use Single Shot AF instead.