In TreeView the selected and checked items have to be provided as IEnumerable<object>.  This can make things a bit of a pain if you have for example outside events that are also trying to change the list of checked items. Not insurmountable or hard but just a pain.

For example to remove an item since IEnumerable is immutable you to have to completely re-assign the collection.  SelectedItems = SelectedItems.Where[Some condition] .  Instead of SelectedItems.Remove, add etc.

I realize the reasons you are binding to IEnumerable<object> and not using generics 

I propose adding "CheckedField" and "SelectedField" in your observable treeview binding and then we would not have to pass in Checked / Selected Items at all and just bind those fields to the Data we are passing in.  Make life a lot easier.

The same thing likely applies to some other controls that have the same problem.  So keep it consistent.