Unable to sort by term weight within multiple term reference
On further looking at this issue, I decided to approach it from a different angle. Without any modifications to my view, which has no sort order defined, I installed and enabled the Taxonomy Term Reference module (https://www.drupal.org/project/term_reference_sortable). 

Using the above module and setting my Menu Categories term reference to use this widget, I found the order I selected is reflected in my view.