ACR WDB TWIN DEP ALTERNATE ARPT OF LNDG WITHOUT AN OVERWT LNDG INSPECTION.

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APCHING IOW AT 39000 FT; FLT ATTENDANT RPTED PAX UNCONSCIOUS. CAPT AND DOCTOR ON BOARD DECIDED TO DIVERT TO MCI FOR HEART ATTACK. WE DECLARED AN EMER AND EXCEEDED 250 KTS BELOW 10000 FROM 10000 FT TO 7500 FT AT 280 KTS TO EXPEDITE LNDG. LNDG NORMAL; DID NORMAL WALK AROUND PREFLT; DISPATCH RELEASE; AND REPLACED USED MEDICAL KIT AND OXYGEN. GND TIME BLOCK TO BLOCK 37 MINS. AFTER TKOF FROM MCI TO LAX; WITH A FULL LOAD OF CONTINUING PAX; WE PULLED OUT THE FLT OPS MANUAL AND BEGAN FILLING OUT CAPT RPT TO THE COMPANY. WE ONLY THEN DISCOVERED WE HAD INADVERTENTLY MADE AN OVERWT LNDG AT 278000 POUNDS AND EXCEEDED THE LNDG LIMIT OF 272000 POUNDS. WE CONTACTED MAINT ON COMMERCIAL RADIO RADIO AND ASKED A FLT MGR UPON ARR AT LAX. IT IS UNUSUAL TO HAVE A LNDG WT PROBLEM WITH THE TWIN WDB. MAINT; DISPATCH; AND CREW DID NOT CATCH THE MISTAKE. INSPECTION AT LAX TURNED UP NO IRREGULAR ITEMS ON THE OVERWT LNDG CHK. PERHAPS A COMPUTER PROGRAM ALERTING DISPATCH AND CREWS COULD GENERATE A RPT ON THE OUTBOUND FLT PLANS FOR DIVERSIONS AND OFF-RTE EMERS. LNDG FLIP CARDS ARE DIFFERENT SHADING COLOR FOR OVERWT SPDS; BUT MISSED MY ATTN.