B737 FO OVERSHOT DEP INTERMEDIATE ALT AND AS THE CAPT WAS INSTRUCTING FO TO CORRECT; ATC ISSUED ADVISORY OF TFC ABOVE AND THE TCASII RA COMMANDED A CLB. SINCE THE TFC WAS IN SIGHT; THE CAPT THOUGHT IT BEST TO RETURN TO ASSIGNED.

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DEPARTING MDW ON THE LAST LEG OF A 4 DAY TRIP; THE FO WAS HAND FLYING. WE FOLLOWED SEVERAL HDG CHANGES AND 1000 FT INCREMENT CLBS. WE WERE CLRED TO 4000 FT FROM 3000 FT. CLBING THROUGH APPROX 3700 FT; ATC CALLED TFC OUT ABOVE US. I LOOKED OUT FOR THE TFC AND SPOTTED HIM. I LOOKED BACK AT THE INSTS AND SAW THAT THE FO HAD CLBED THROUGH 4000 FT. I STATED FOR HIM TO CORRECT BACK TO 4000 FT. AT THIS TIME WE RECEIVED AN RA TO 'CLB; CLB.' I LOOKED OUT FOR SECONDARY TFC WHILE WATCHING OUR INITIAL TARGET. THE FO HAD PULLED BACK ON THE YOKE TO ADHERE TO THE RA. BY THEN; WE WERE CLBING TO 4600-4700 FT. I HAD TO MAKE THE DECISION TO PUSH ON THE YOKE USING THE INFO I HAD. WE DSNDED BACK TO 4000 FT. THE CTLR STATED THAT WE WERE CLRED TO 4000 FT; AT THE SAME TIME I STATED WE WERE REACTING TO A TCASII ADVISORY. THERE WAS NO OTHER DISCUSSION. MAKING A SMALL ALT CORRECTION BECAME A SERIOUS DECISION TO MAKE AFTER THE RA. I FEEL I DID WHAT I HAD TO DO. I BELIEVE THAT THE TCASII MAY HAVE BEEN TRYING TO CLB US OVER THE TFC. I WAS IN VISUAL CONTACT WITH THE TFC THE ENTIRE TIME.