A320 CREW HAD AN NMAC WITH A BE35 IN PVD CLASS E AIRSPACE.

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SCHEDULED ACR DSNDING INTO PVD. CLRED TO DSND TO 8000 FT. WE OVERHEARD ATC ASK OTHER ACFT VFR AT 8500 FT AS TO HIS INFLT VISIBILITY. THE OTHER ACFT STATED '4 MI.' THE CTLR ADVISED THIS ACFT THAT THERE WAS AN AIRLINER DSNDING THROUGH HIS ALT. SHORTLY THEREAFTER; WE NOTICED THIS ACFT (WE WERE DSNDING AT 1500 FPM THROUGH 9000 FT). AS PF; I INITIATED AN IMMEDIATE PULL-UP WITHOUT WAITING FOR THE TCASII BECAUSE WE WERE RAPIDLY CONVERGING HORIZLY AND VERTLY. I CLBED OVER THE INTRUDER. WHEN I TRIED TO LEVEL; WE RECEIVED A TCASII RA TO MONITOR VERT SPD; AND WERE SOON CLR OF CONFLICT. NOTE: THE INFLT VISIBILITY WAS ZERO. THE OTHER PLT WAS FLYING VFR AND RPTING 4 MI WHEN IT WAS ZERO. THIS CONTRIBUTED TO LULLING THE CTLR INTO COMPLACENCY. I EXERCISED MY CAPT'S AUTH TO PROACTIVELY MANEUVER AWAY FROM THE CONFLICT AND CLBED CONTRARY TO CLRNC. SUPPLEMENTAL INFO FROM ACN 553119: APPROX 20 NM SW OF PVD; PVD APCH CALLED TFC DSNDING; AN AIRBUS TO MY R. I XMITTED 'I DID NOT SEE THE TFC.' THE AIRBUS PLT XMITTED TO APCH HE WAS IMC AND HAD A TCASII ALERT THAT MADE HIM CLB AND THAT I MUST BE IN INST CONDITIONS. PVD APCH THEN ASKED ME MY VISIBILITY TO WHICH I REPLIED; 'MY VISIBILITY IS 3-4 MI.' THE AIRBUS PLT CONTINUED QUESTIONING THE SIT WITH PVD APCH. PVD APCH SAID NOTHING ELSE TO ME OTHER THAN HANDING ME OFF TO THE NEXT CTLR.