So, just following up on this several years later for anyone who might be working the same issue, the setting for Annotation Objects > xxxx Tag will control both the Tag Head and Leader lineweights. To get separate lineweights for the tag head and leader, you need to create a subcategory in the Tag Family for the Head, and make it heavier, then put the tag head linework on that subcategory. Then the graphical settings for the Category of the Tag will control the leader lineweight, and a subcategory of it will control the head lineweight. It's kinda backwards, but you can get there.
My other CAD is a Cadillac and I like to Revit to the Max!