THE PILOT IN COMMAND OF THE FLIGHT, WHO HAD NOT PERSONALLY PERFORMED A VISUAL CHECK OF THE FUEL QUANTITY PRIOR TO DEPARTURE, AND WHO HAD EXPERIENCED UNEXPECTED STRONG HEADWINDS ALONG THE ENTIRE ROUTE, REFILED FOR A MORE DISTANT AIRPORT WHILE ABOUT 15 MINUTES SHORT OF THE ORIGINAL DESTINATION. THE FLIGHT CONTINUED TO EXPERIENCE STRONG HEADWINDS WHILE CONTINUING EN ROUTE TO THE REFILED DESTINATION WHERE THE WEATHER WAS REPORTED TO BE CONSIDERABLY LOWER THAN THAT AT THE ORIGINAL DESTINATION. FUEL EXHAUSTION OCCURRED WHILE THE AIRCRAFT WAS ON ILS FINAL TO THE REFILED DESTINATION.