THE PLT HAD CALLED HIS HOME BASE & WAS TOLD THAT FOG WAS BEGINNING TO MOVE SHOREWARD & THAT THE INTENDED DESTINATION, (WATERFORD, CT) WOULD NOT REMAIN VFR FOR LONG. THE PLTS OF N6877J & ANOTHER ACFT CHOSE TO DEPART IMMEDIATELY. BEFORE ARRIVING, FOG HAD MOVED IN, SO THEY ELECTED TO DIVERT TO FISHERS ISLAND, NY. DURING THEIR ARRIVAL TO FISHERS ISLAND, THE PLT OF N6877J WAS LEADING. IT WAS A DARK NIGHT, BUT THE PLT OF THE FOLLOWING ACFT ESTIMATED THAT THE VISIBILITY IN THAT AREA WAS APRX 15 MI. WHILE THE PLT OF THE 2ND ACFT WAS STILL AT 3000 FT, HE OBSERVED N6877J ON A 1 MI BASE LEG FOR RWY 19 WHEN IT CRASHED. HE STATED THAT THE ACFT APPEARED TO DO A CARTWHEEL ON THE WATER WHEN IT IMPACTED. TWO ACFT WHEELS & THE PLTS BODY WERE RECOVERED, BUT THE MAIN WRECKAGE WAS NOT FOUND. THE ARPT WAS EQUIPPED WITH MEDIUM INTENSITY RWY LIGHTS, BUT THERE WERE NO VASI LIGHTS INSTALLED & NO INSTRUMENT APPROACH FOR THE ARPT.