A B767-300 FLT CREW; EARLY IN A TRANS-OCEANIC FLT; RECEIVED A 'WX RADAR WEAK' ERROR MESSAGE. THEY DECLARED AN EMERGENCY AND DIVERTED TO A SUITABLE AIRPORT.

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RADAR FAILURE PRIOR OCEANIC XING. 10 MINS AFTER DEPARTING; TURNED WX RADAR ON AND RECEIVED WX RADAR WEAK MESSAGE. TESTED RADAR AND RECEIVED WX FAIL MESSAGE. CONTACTED MAINT WHO ADVISED WX RADAR WEAK WAS AN IMPENDING FAILURE MESSAGE. CONTACTED DISPATCH WHO COORD OUR DIVERSION TO ZZZ TO FIX RADAR/CHANGE ACFT AND ADVISED THEM OF OUR OVERWT STATUS AND OUR NEED TO DUMP FUEL. NOTIFIED ATC AND BEGAN FUEL DUMP OVER ZZZZZ INTXN AND TERMINATED PRIOR TO LANDFALL NEAR XYZ. DUMPED REMAINING CTR TANK FUEL (13000 LBS) IN 5 MINS AT FL350. CONSULTED PERFORMANCE MANUAL QUICK TURNAROUND WT BRAKE COOL-DOWN CHART AND THEN DSNDED TO FL210 TO BURN OFF ADDITIONAL FUEL TO AVOID 75 MIN TKOF DELAY REQUIREMENT FOR LNDG WTS ABOVE 328000 LBS. INFORMED PURSER ON OUR OVERWT LNDG STATUS AND HAD CABIN CREW BRIEF PAX ON PRECAUTIONARY EMER LNDG PROCS. NOTIFIED ZZZ APCH CTL OF OUR OVERWT LNDG STATUS; DECLARED EMER AND REQUESTED CFR DUE TO SAME. AFTER 20 MINS OF VECTORING FOR FUEL BURN-OFF; RECEIVED PERMISSION TO LAND. XFERRED CTL OF THE ACFT FROM THE FO TO CAPT AND LANDED FLAPS 30 DEGS WITH AUTO BRAKES AT A TOUCHDOWN SINK RATE OF 75 FPM. HAD CFR CREW CHIEF INSPECT BRAKES AFTER UNEVENTFUL LNDG AND THEN TAXIED TO GATE.