B777 FLT CREW EXECUTES A GAR DUE TO TFC AND VISIBILITY AT SFO.

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WE WERE CLRED FOR THE ILS RWY 28R APCH TO SFO. WE WERE ASKED IF WE HAD TFC IN SIGHT ON APCH TO RWY 28L; WE RESPONDED AFFIRMATIVELY. AT APPROX 1800 FT MSL NEAR THE FAF; THE CTLR ASKED IF WE STILL HAD THE TFC IN SIGHT FOR RWY 28L. AT ABOUT THE SAME TIME THAT ACFT WENT BEHIND OR INTO CLOUDS; WE RPTED THAT THE TFC WAS NO LONGER IN SIGHT. WE WERE INSTRUCTED TO MAINTAIN 2000 FT; SO WE CLBED TO 2000 FT. SECONDS LATER; WE WERE TOLD TO RE-INTERCEPT THE GS AND WERE RECLRED FOR THE APCH. WE ADVISED THAT WE WERE UNABLE DUE TO WX AND POSITIONING IT WOULD HAVE CREATED AN UNSTABLE APCH AND WERE INSTRUCTED TO GO AROUND; CLB TO 5000 FT RADAR HDG. AT THAT TIME WE ADVISED NORCAL OF MINIMUM FUEL. ON THE GAR; WE RECEIVED LOW FUEL WARNING ON THE L ENG. FUEL WAS AT 13.7. VECTORED FOR LENGTHY DOWNWIND AND LANDED UNEVENTFULLY ON RWY 28R WITH FUEL AT 10.4. THERE APPEARED TO BE AN UNUSUAL LACK OF COMS BTWN NORCAL SECTORS REGARDING HDGS AND AIRSPDS DURING APCH AND CHANGING WX CONDITIONS DURING THE APCH CONTRIBUTED TO THE GAR AND LOW FUEL SITUATION. IN MY OPINION; BECAUSE OF THE INCREASING LOW STRATUS; PARALLEL APCHS SHOULD HAVE BEEN DISCONTINUED SOONER.