APPARENTLY FALSE EICAS R ENGINE SHUTDOWN MSG DURING CLIMB OUT CAUSES B767-300 TO RETURN TO DEP ARPT FOR OVERWEIGHT LNDG AND MAINT.

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TAXI AND TKOF WERE UNEVENTFUL. AFTER CLEAN-UP; WITH CLB PWR STABILIZED FOR ABOUT 1 MIN; WE GOT A R ENG SHUTDOWN EICAS MESSAGE ALONG WITH A R ENG VALVE LIGHT ILLUMINATED. ALL OTHER R ENG INSTS; INCLUDING FUEL FLOW; APPEARED WITHIN NORMAL PARAMETERS. WE LEVELED OFF AT APPROX 10000 FT AND GOT VECTORS FROM APCH TO SORT IT OUT. WE CONSULTED THE QRH AND FOLLOWED THE PROCS TO ATTEMPT TO REMEDY THE SITUATION TO NO AVAIL. WE CALLED DISPATCH AND MAINT; BUT THEY COULDN'T DETERMINE WHY WE WERE GETTING THE ENG SHUTDOWN MESSAGE. WE DISCUSSED HVY WT LNDG OPTION WITH MAINT; AND AFTER CONSIDERING ALL OF THE FACTORS; DECIDED IT WOULD BE SAFE AND PRUDENT TO EXECUTE AN OVERWT LNDG. WE TOUCHED DOWN WITH A MINIMUM RATE OF DSCNT AT ABOUT 308K LBS AND TURNED OFF ABOUT 3/4 OF THE WAY DOWN THE RWY. OUR BRAKE TEMP INDICATORS NEVER SHOWED OVER 1 THROUGH SHUTDOWN. AN OVERWT LNDG ENTRY WAS MADE IN THE LOGBOOK. MAINT TINKERED WITH THE R ENG FOR BOUT 1 HR; COMPLETED AN OVERWT LNDG INSPECTION; AND THEN WE CONTINUED UNEVENTFULLY.