A B737-700 CREW EXPERIENCED AN AILERON DEAD BAND BTWN PLUS OR MINUS 0-4 DEGS OF AILERON MOVEMENT. NORMAL INPUT BEYOND 4 DEGS.

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IT WAS THE FO'S LEG FROM ZZZ. UPON ROTATION DURING TKOF WITH AN APPROX 15 KT L XWIND; THE FO NOTICED A SIGNIFICANT ROLL DUE TO UNRESPONSIVE AILERON INPUT FOR XWIND CORRECTION. THE FO RECOVERED BY USING R AILERON AND RIGHTING THE WINGS. THE FO THEN TOLD ME THE AILERONS SEEMED 'SLOPPY' AND ASKED ME TO TRY FLYING IT AT APPROX 1200 FT AGL. I TOOK CTL OF THE ACFT AND NOTICED THE SAME THING. BASICALLY THE AILERONS FELT AS THOUGH THERE WAS A DEAD BAND BTWN 4 DEGS L AND R DEFLECTION. ONCE I CONTINUED ROLL INPUT BEYOND 4 DEGS; THE CTLS THEN FELT MORE NORMAL; AND ROLL WAS CTLABLE BEYOND THE 4 DEG POINT. THE ACFT REMAINED IN POSITIVE CTL THROUGHOUT THE FLT; THE AILERONS JUST FELT UNRESPONSIVE IN THIS 4 DEG RANGE OF MOTION EITHER SIDE OF CTR. WE CLBED TO 10000 FT AND DISCUSSED THE PROB. I CHKED CIRCUIT BREAKERS AND DID SOME TROUBLESHOOTING BUT COULD NOT FIND A SOLUTION TO THE PROB. WE THEN DECIDED TO DECLARE AN EMER AND RETURN TO ZZZ. I COMMUNICATED WITH THE FLT ATTENDANTS; OPS AND MAINT WHILE THE FO FLEW. I THEN TOOK OVER CTL OF THE ACFT AND MADE A NORMAL APCH AND LNDG IN ZZZ ON RWY 25. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT THE AILERON TRIM ACTUATOR WAS REPLACED AND SEVERAL DAYS LATER THE AILERON CTRING BEARING WAS REPLACED. NO FURTHER DISCREPANCIES WERE WRITTEN AGAINST THE AILERON CTL SYS.