I tracked the problem to a System.Windows.Forms.TrackBar on the parent control. The track bar had a maximum over 200,000,000. When I decreased the maximum to 100,000,000, it used about half the memory. Setting the maximum around 1,000,000 used a more reasonable amount of memory.
The checkbox.Visible threw me off. It appears that the applications was creating the control and the memory for it at the point the checkbox.Visible became true, but the checkbox itself had nothing to do with the problem.