MLG EXPERIENCES A TCASII WARNING WHEN THEY DON'T TURN AS TIGHT AS DESIRED BY ATC.

Narrative

FO WAS FLYING LEG. HVY MLG WITH REDUCED FLAP TKOF BECAUSE OF WT. TWR CLRED US FOR TKOF RWY 12R WITH L TURN TO 340 DEGS AND 'KEEP IT TIGHT.' SID SAYS INITIAL HDG MUST BE COMPLETED WITHIN 3 DME OF HOU. WE WERE TRYING OUR BEST TO KEEP IT WITHIN 3 DME. ACFT NOT PERFORMING WELL DUE TO NOISE ABATEMENT PWR SETTING AND HVY WT; BUT WE WERE RIGHT ON THE 3 DME. ABOUT 1/2 WAY THROUGH TURN TWR TOLD US TO TIGHTEN THE TURN. WE REALLY COULDN'T DUE TO OUR SPD. BEFORE I COULD ANSWER; ANOTHER CTLR VOICE (FEMALE) INTERRUPTED AND TOLD US TO CLB NOW WITHOUT DELAY TO ASSIGNED ALT OF 4000 FT. THEN THE TCASII SOUNDED 'TFC; TFC.' I ACKNOWLEDGED CLB AND TFC CONFLICT PASSED. THE HOU DEP SAYS TO INFORM CTLR BEFORE TKOF IF UNABLE TO KEEP TURN WITHIN 3 DME. WE DID KEEP WITHIN 3 DME; BUT WERE UNABLE TO KEEP IT TIGHT ENOUGH FOR HIM. I STILL DON'T KNOW HOW TIGHT HE WANTED IT; BUT ASSUMED 3 DME WOULD BE ENOUGH. I DON'T THINK ATC REALIZES A GROSS WT TKOF IN AN MLG OR MOST ANY OTHER TRANSPORT JET TAKES SOME TIME AND DISTANCE AND DURING THE CLEANUP WE ARE LIMITED IN OUR ANGLE OF BANK.