B757-200 OVERWATER FLT EXECUTED MISSED APCH DUE TO POOR VISIBILITY AT DEST; AND THE FLT CREW DIVERTED. FLT LANDED WITH 25 MIN FUEL REMAINING.

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FLT TO LIH. HAD OVERBURN; PLUS SIGNIFICANT WIND BUST; STILL SHOWED LNDG LIH WITH 6.0 FUEL. ATIS ADVERTISED 5 MI AND 1200 FT BROKEN. FLEW VOR RWY 21 APCH TO MINIMUMS TO A MISSED APCH DUE TO RAIN SHOWERS AND POOR VISIBILITY. FLEW STRAIGHT TO HNL AND BLOCKED IN WITH 2.6 FUEL (WE HAD ADDED 1.0 CLRED FUEL). MANY CONTRIBUTING FACTORS: WRONG BURN RATE FOR ACFT; FLT PLAN PLANNED AT MACH .77; WINDS MORE THAN DOUBLE FORECAST IN SOME AREAS; ATIS AT ARR INACCURATE; BAD ARR FORECAST FOR LIH (NO ALTERNATE). I AM DONE PLANNING MINIMUM FUEL AT ARR TO SAVE THE COMPANY MONEY. IT ISN'T SAFE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: REPORTER STATED THAT MACH .77 FLT PLAN WAS SLOWER THAN USUAL; WHICH DID NOT ALLOW FOR ADJUSTING CRUISE SPEED TO CONSERVE FUEL. WHEN WINDS WERE DISCOVERED TO BE LESS FAVORABLE DURING CRUISE; LANDING FUEL WAS STILL PROJECTED AT APPROX ONE HOUR FUEL REMAINING AT TOUCHDOWN. EVEN THOUGH THE ATIS FOR ARRIVAL INDICATED 5 MILES VISIBILITY; A RAIN SHOWER PREVENTED THE FLT CREW FROM OBTAINING VISUAL CONTACT WITH THE ARPT; SO THE FLT CREW DIVERTED TO HNL. AN ALTERNATE WAS NOT PLANNED FOR THE DEST; AND THE CLEARED FUEL WAS BASED UPON HAVING SUFFICIENT FUEL ONBOARD AT THE PET. THE FLT CREW DECLARED MIN FUEL; AND THEY LANDED WITH APPROXIMATELY 25 MIN FUEL REMAINING.