NMAC RPTED BY PIC OF A DEP B757 WITH A PREVIOUSLY DEPARTED C-150 CLBING AT 3000 FT; 2 NM SW OF IAD; VA.

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TAXIED TO RWY 19L AND HELD ON TXWY FOR POSSIBLE ATC RERTE (NO RERTE WAS EVER RECEIVED). CESSNA 150/170? WAS CLRED FOR TKOF ON RWY 19L FROM INTXN H1 ACR AIRBUS CLRED FOR TKOF RWY 19L. WE CLRED TKOF RWY 19L FROM INTXN H1. TWR: 'ACFT X CLRED FOR TKOF RWY 19L FROM INTXN H1; TURN TO HDG 230 DEG AS SOON AS PRACTICAL AFTER TKOF. I HAVE A SMALL CESSNA HDG SW AND I NEED YOU TO TURN INSIDE OF HIM.' ACFT X: 'CLRED FOR TKOF HDG 230 DEGS.' AFTER LIFTOFF; I MAINTAINED V2 +15 KTS AND FLAPS 5 KTS AND TURNED TO HDG 230 DEGS; TURNING AT 400 FT AGL. STARTED TO ACCELERATE FOR FLAP RETRACTION AT 800 FT AGL. SHORTLY AFTER THIS; THE FO SAID 'I SEE THAT CESSNA AT 12 O'CLOCK HIGH POS. I ALSO GOT A VISUAL AT THAT TIME. AT THIS TIME; I REALIZED WE WERE ON A COLLISION COURSE. I MADE AN ABRUPT R HAND TURN TO HDG 260 DEGS AND AN ABRUPT LEVELOFF AT 2600 FT MSL. DURING THIS SAME TIME PERIOD; THE TCASII TA (NO RA) SOUNDED AND IAD TWR TURNED US OVER TO POTOMAC DEP. DEP ASKED IF WE HAD THE CESSNA. WE REPLIED THAT IT WAS BEHIND AND ABOVE US; AND THAT WE PASSED WITHIN 400 FT AND WOULD BE FILING A NEAR MISS. CALLED IAD TRACON 6 HRS LATER. A CTLR TOOK MY NAME; ADDRESS; AND PLT CERTIFICATION NUMBER. CALLED FLT OPS TO CONFIRM I HAD CALLED FAA.