MD88 RWY 34L DEP FROM DEN EXPERIENCED CONFLICT AT 7000 FT WITH TFC ON BASE FOR OPPOSITE PARALLEL RWY 16L.

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WE DEPARTED DEN RWY 34L WHILE ANOTHER ACFT WAS ON BASE TO FINAL WITH CLRNC TO LAND OPPOSITE DIRECTION ON PARALLEL RWY 16L. TWR POINTED OUT THE TFC TO US PRIOR TO TKOF AND ADVISED US IT WOULD NOT BE A FACTOR. WE WERE GIVEN A HDG OF 355 DEGS AND CLRED FOR TKOF. AT APPROX 1000 FT AGL WE WERE GIVEN A 10 DEG R HDG CORRECTION. SHORTLY AFTER; WE RECEIVED A TCAS TA ADVISORY; FOLLOWED BY TWR DIRECTING A MAX CLB FROM US UNTIL THROUGH 7000 FT MSL. THE OTHER ACFT ASKED TWR ABOUT OUR SEPARATION AND TWR ADVISED THEM WE WOULD BE ABOVE THEIR ALT. DUE TO THE DARKNESS; IT WAS DIFFICULT TO SEE OUR ACTUAL HORIZ SEPARATION. WE APPEARED TO CROSS THEIR FLT PATH APPROX 500-700 FT BEHIND AND ABOUT 1000 FT ABOVE THEM. THERE WERE SEVERAL CONTRIBUTING FACTORS: 1) ALTHOUGH THE START OF THE TRIP; IT WAS XA00L AND CERTAINLY OUR ALERTNESS WAS IMPACTED. 2) WE REQUESTED AN OPPOSITE DIRECTION TKOF ON RWY 34L DUE TO WT LIMITATIONS. 3) WE SHOULD HAVE DELAYED AND TWR SHOULD NOT HAVE APPROVED OUR TKOF WITH A KNOWN ACFT ON BASE TO FINAL FOR THE PARALLEL OPPOSITE DIRECTION. 4) FINALLY; WE SHOULD HAVE REQUESTED A SLIGHT L (WESTERLY) HDG RATHER THAN THE 5 DEGS R CORRECTION ISSUED BY TWR WITH OUR TKOF CLRNC.