RWY EXCURSION DURING A NIGHT OP BY A B737 FO WHEN LOSING DIRECTIONAL CTL ON TOUCHDOWN IN HVY RAIN WITH WINDS VARIABLE DUE TO TSTM ACTIVITY NEAR GPT.

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FIRST TIME IN GPT. NO WINDSHEAR RPTED. I RECALL ATIS RPTING WX AS 2000 FT SCATTERED; 5000 FT OVCST; 3-5 MI; WIND NE AT 10 KTS GUSTING TO 20 KTS. APCHING ARPT TSTMS N; NW; SW; AND E OF ARPT. APCH WANTED TO TURN US N FOR TFC. WX CONCERNS WOULD NOT ALLOW THAT. WE DID A 360 DEG TURN DSNDING TO 2000 FT AND ROLLED OUT ON AN INTERCEPT HDG FOR RWY 14 LOC. WE WERE AT LEAST 7 MI OUT WITH RWY IN SIGHT. RAIN RPTED AT ARPT; HOWEVER RWY ENVIRONMENT; STILL IN SIGHT. APCH WAS STABLE WITH WIND ADDITIVE FOR GUST. DURING LNDG FLARE RAIN CAME DOWN AND VISIBILITY DROPPED WAY DOWN. ACFT VEERED TO R. I CORRECTED L AND SAW R SIDE RWY LIGHTS APCHING. I FELT R WHEELS LEAVE RWY. CORRECTED BACK ONTO RWY; THOUGHT WE GOT CLOSE TO L SIDE; BUT NOT OFF. BROUGHT ACFT TO STOP ON CTR OF RWY. CAPT MADE 'REMAIN SEATED' PA. CALLED TWR AND HAD TRUCKS INSPECT ACFT FOR DAMAGE BEFORE WE MOVED. FOUND NO DAMAGE ON R SIDE OF ACFT AND TAXIED TO GATE. SUPPLEMENTAL INFO FROM AN 622358: MADE STANDARD CALLOUTS; BUT JUST AS WE FLARED WE HIT HVY RAIN. HAD VISUAL REF ON THE SIDE RWY LIGHT (NO RCL) ACFT DRIFTED R AND MADE CONTACT (INSTANTLY). I THOUGHT THE R MAIN WAS OFF 5-10 FT; VERY ROUGH AND I WASN'T SURE OF LATERAL STABILITY SO A GAR WAS NOT AN OPTION. CONTACTED TWR; HAD THEM ROLL THE TRUCKS TO INSPECT FOR DAMAGE. EMPHASIZED R SIDE AND NO DAMAGE FOUND. TAXIED TO GATE; SUBSEQUENTLY MAINT FOUND SCRAPES ON #1 ENG AND DAMAGE TO THRUST REVERSER SLEEVE.