(Putting the full solution here so people who haven’t got as far as enabling the web inspector will see it.)
First ensure that the Develop menu is enabled: in the Advanced pane in Safari Preferences (Cmd + ,) select “Show Develop menu in menu bar”.
Then, from the Develop menu select Show Page Resources (Cmd + Alt + A). Then, in the top right corner of the view, just under the tab bar, there is a button to “Show the details sidebar” (Cmd + Alt + 0). Click it.
Then you can select each resource from the left sidebar and the headers will appear in the right sidebar. You may need to refresh the page to see them initially.