B737 Captain reported on climb out the aircraft had a left rolling tendency and the yoke had several dead spots requiring more than normal control forces to get aircraft to respond. Flight crew diverted and completed a normal landing.

Narrative

On walk around First Officer noticed fluid near the aileron control unit in the wheel well. I went to check and found what appeared to be hydraulic fluid wearing from the actuators. A ELB entry was made. Local maintence had us pressurize the system and operate the roll input. About 10-15 full deflection inputs were made and the writeup was cleared. (A system hydraulic level was slightly lower than B. A had about 83% vs B at 90%.)Normal F25 takeoff was performed; with aircraft wt about 150;000#. On climb out noticed the aircraft had a slight tendency to roll left. There as a noticeable dead spot between 2 units left of top to top on the yoke; which had very little roll to the aircraft. Forces past top to the right were stiff and noticeably more force than normal was required to get the aircraft to respond.Climb out and initial cruise were performed in the center of airspeed window. Pitch and rudder inputs/ responses were normal.Decision was made to proceed to ZZZZ vs ZZZZ1 due to runway length; aircraft weight; and airport resources. [Priority handling requested] with ZZZ Center. Dispatch was contacted via SATCOM and a phone patch to Maintenance Control was initiated. The situation was discussed; and I told Dispatch that we would contact them shortly to discuss the plan of action with the Chief Pilot. The Chief Pilot was contacted about 30 minutes after takeoff and we coordinated our game plan to continue to ZZZZ.The F/O and I discussed the checklist; passenger instruction; F/A awareness; and course of action into ZZZZ.The F/As were to remain seated except to prepare the cabin for arrival. A briefing was given first on the intercom and later in person prior to descent. No passenger services were to be performed. Passengers were seated except for a 15 minute period prior to top of descent for lavatory usage.RNAV was to be performed to [Runway] XXL as the ILS was OTS. XXL was chosen due to runway length. The field was sighted 40 miles out. Being restricted to the RNAV was the only quandary we had as the FM directed A/P and A/T off directly contradicts the FM guidance on A/P usage during a NP (non-precision) approach. Fortunately ZZZZ was VMC that evening. Flap 15 landing was performed. Right roll past center was noticeably more difficult at the slower speeds.Normal touchdown and rollout.ZZZZ aircraft rescue and firefighting directed us to stop on the runway for an aircraft inspection. Which seemed at the time silly as the situation involved a flight control issue and normal taxiing was noted.Overall the situation went very well with coordination of ATC; Company operations in ZZZ; and on ZZZZ.