I notice that when I change the font weight for the Nav Font Weight in the Customizer, it doesn’t recognize that anything has changed and the “Save” button is greyed out. Also, when I go back into the Nav Font Weight setting the next time I login to the WP Admin, it defaults to “700” even though the Menus still maintain their old weight setting appearance.
Sure enough, I can recreate the issue on your site as well as on my localhost. When I tested first, I had Bold selected so it didn’t make any difference. I’ll go ahead and submit a bug report for this. Thanks for pointing it out!