It depends on your resizing requremnts. The anchors can only handle position of the objects. They cannot handle changing a font size, e.t.c.
Are you sure that container B is inside container A? What are anchor values for containers and label?

>I have a container (A) with a label and a line. I have anchored both the object to this container. In turn this container (A) is anchored to container (B). When I run the form that has container (B) on it. As soon as I resize the form the resize() code is fired and container (B) is rightly resized but the container (A) still stays where it is (I have just recently added this container and I have not written any resize code hoping anchor is supposed to do it).