The direct answer is to change your If line to also check that the CC is a checkbox
Code:
If ContentControl.Tag <> "" And ContentControl.Type = wdContentControlCheckBox Then
You could also use other methods to identify when a checkbox needs to change the visibility of the secondary area. All CCs have both a Tag and Title property so you could use one of these as the trigger for the macro and the other for the bookmark region.
eg
Code:
If ContentControl.Tag = "SectionShowHide" then
ActiveDocument.Bookmarks(ContentControl.Title).Range .Font.Hidden = Not ContentControl.Checked