B737 Captain reported an air turn back after a fuel imbalance was detected during climbout.

Narrative

It was my leg to fly and everything was standard and uneventful through takeoff and departure; our fuel indicated 23.8k before departing. We had fuel in the center tank and both center pumps were on. On climbout; the Captain noticed a slight fuel imbalance; with the right tank lower; and shortly after that the 'fuel imbalance' annunciator light turned on. We were climbing through about 16000 ft. when we started troubleshooting the issue. It appeared by the totalizer and right tank quantity indicators that we were either burning fuel from the right tank or had a fuel leak from the right wing or engine.As we climbed the imbalance worsened as the totalizer also indicated higher fuel loss than expected. The imbalance worsened to about 1500 lbs; and we attempted to balance the tanks by transferring fuel from left to right. The increase in fuel imbalance was abated using this method; and it also started to reduce the imbalance.We ran the QRH checklist for a potential fuel leak; deciding not to shut down the right engine to expedite the divert and due to our heavy weight; suspecting that would be less safe than keeping it running. We requested priority handling and returned to ZZZ via vectors to a visual approach Runway XX; with the ILS used as a backup.It was night and the weather was VFR. Upon an uneventful landing I utilized the left engine thrust reverser and we stopped on the runway and shutdown the right engine as a precaution. Emergency vehicles met the airplane to inspect the right wing and engine; nothing noteworthy was discovered. We taxied to the gate and shutdown the left engine; non-normal complete.CRM between myself and the Captain was excellent throughout the flight. The Captain read all non-normal checklist aloud and asked if I had any inputs or questions when appropriate. The demeanor in the cockpit was professional; calm; and business-like at all times as we worked our way through solving the problem and executing a divert back to ZZZ. The decision not to shut down the right engine was discussed at length and we both concluded that due to cockpit indications and our heavyweight the best course of action was to land immediately and shut it down on the runway. In retrospect this proved to be the correct call after maintenance personnel discovered multiple faults with the fuel totalizer and both wing compensators causing major fuel system instrument irregularities; and in fact no fuel leak was present.