A B757 CAPT HELPED HIS FO; THE PF; TAKE EVASIVE ACTION DURING AN RA IN N90'S AIRSPACE.

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LEVELING AT 4000 FT; RECEIVED A TCASII TFC ALERT FOLLOWED BY A CLB RA. TFC WAS A BEECH BARON AT 10 O'CLOCK POS; COMING UP FROM BELOW. FO WAS FLYING AND COMPLIED IMMEDIATELY WITH THE RA; BUT I COULD SEE THE TFC CLOSING AND I POINTED IT OUT TO HIM. (TFC WAS INITIALLY OUT OF HIS VIEW SINCE HE WAS LOOKING CROSS COCKPIT AND DOWN.) HE EXECUTED A CLBING R TURN TO AVOID COLLISION. MEANWHILE; THE TCASII CHANGED ITS MIND AND STARTED SAYING TO DSND. THE NEAREST POINT OF APCH WAS APPROX 1000 FT. THE OTHER ACFT BANKED L AT ABOUT THAT POINT; BUT WE WERE ALREADY TURNING AWAY AND CLBING. IN MY OPINION; THE RA THAT WE GOT FROM THE TCASII WAS TOO LITTLE TOO LATE AND WOULD NOT HAVE KEPT US APART IF WE HAD NOT TURNED. WE WERE HANDED OFF TO TWR IMMEDIATELY AFTER THAT; AND WERE BUSY WITH THE APCH AND LNDG. I DID NOT ASK ATC FOR A NEAR MIDAIR COLLISION RPT. THEY DID ASK ABOUT OUR MANEUVER AND WE TOLD THEM THAT WE HAD TO AVOID ANOTHER ACFT. I THINK I HEARD THEM TALKING TO THE OTHER ACFT ABOUT IT ALSO; BUT I CANNOT BE SURE. WE WERE ON A VISUAL APCH IN VFR CONDITIONS; SO THERE WAS NO CLRNC DEV. I KNEW WE WOULD FILE A RPT LATER ON AND DID NOT WANT TO BE DISTR AT THAT PHASE OF THE APCH AND LNDG TALKING TO ATC ABOUT IT.