Where/how do I edit/influence the permissions which dictate which Web Parts users see when they choose to add a web part to one of their pages in SharePoint 2010?
In Site Settings, choose Web Parts. Find and edit the .dwp or .webpart item for the Web Part you're wanting to restrict. On the Edit tab, click Manage Permissions in ribbon.
This doesn't affect the visibility users have to instances of this Web Part that have been placed on a page.