MLG HAS A CONFLICT WITH A VFR ACFT PROCEEDED BY A TCASII RA.

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CLRED TO 17000 DIRECT TO DUPONT VOR. CTR ADVISED VFR TFC AT 12500 2 O'CLOCK AND 5 MIS. I SAID WE HAD HIM ON TCASII AND LOOKED OUTSIDE FO'S SIDE WINDOW. I SAID 'I MIGHT HAVE HIM VISUALLY' BUT COULDN'T BE SURE BECAUSE FO WAS FLYING AND PROCEEDING DIRECT DUPONT VOR AS CLRED AND IN TURN I LOST THE TFC I WAS LOOKING AT. FO PROCEEDED TO CLB AND NAV AS CLRED WHEN WE RECEIVED A RA ON TCASII TO MONITOR VERT SPD AND LIMIT CLB TO 500 FT A MIN. FO DID THIS AND TFC PASSED OVERHEAD US; POSSIBLY A BIT BEHIND; AT 1 POINT VERT CLRNC MAY HAVE BEEN ONLY 600 FT. VERY DIFFICULT TO SAY BECAUSE WE WERE PROCEEDING AS CLRED AND ONLY LIMITED CLB RATE BECAUSE OF TCASII; AND WE HAD LOST SIGHT OF THE INTRUDER DURING THE RUN. I'M NOT SURE THAT THIS WAS A NEAR MISS; BUT FEEL THERE WAS SOME MISCOM INVOLVED THAT SHOULD BE RPTED FOR FUTURE REF. I BELIEVE CTR SHOULD NOT HAVE PUT US ON A CONFLICTING COURSE WITH TFC. I DON'T THINK VFR TFC SHOULD NAV THROUGH THE PHILADELPHIA-DCA AREA; ESPECIALLY IN THE HIGHER ALTS. I DON'T THINK I SHOULD HAVE SAID ANYTHING TO CTR EXCEPT REQUEST A VECTOR AROUND THE TFC IF HE THOUGHT IT WAS CLOSE. ALSO THE CTR FREQ WAS VERY BUSY AND THE CTLR OBVIOUSLY HAD A VERY HVY WORKLOAD.