B737-800 First Officer reported fuel imbalance developed during departure climb. First Officer stated the Captain did not perform the Fuel Leak QRH procedure to avoid inflight engine shutdown and the flight returned to the departure airport.

Narrative

Everything appeared normal initially during the climb. The center tank indicated about 1800lbs of fuel upon takeoff - 18;XXXlbs total roughly. Climbing through around 10;000ft we got a 'fuel' caution and noticed the center tanks were already empty. This seemed abnormally fast; but I also didn't think too much into it as we didn't have a ton of fuel in the center tank to begin with. We turned off the center pumps and continued normally. About 10 minutes later we noticed a 'fuel IMBAL (Imbalance)' light under the left fuel quantity. The left tank was about 1;500lbs lower than the right tank and continuing to decrease. We noted the left fuel level at 7.8xlbs. The Captain then looked at the fuel log and saw we were already 1;000lbs short at the first waypoint and still climbing. The Captain mentioned how he had this situation before and it turned out to be a legitimate fuel leak. The Captain turned off the left fuel pumps and opened the crossfeed. The fuel quantity in the left tank should have stabilized and stopped flowing; per prior experience with correcting minor imbalances. However; in this instance it did not stop. Less than a minute later the left fuel level was now at 7.70lbs and still decreasing. The left fuel pumps remained off. We came to the conclusion we had a fuel leak and the Captain assigned me pilot flying. We then divided the cockpit so the Captain could make the necessary notifications. He also began to run the Non-Routine Landing Considerstions Checklist. I talked to ATC and got the airplane set up for the return to ZZZ. At the Captain's direction; I [requested priority handling] with ATC and asked to return to ZZZ. I queried the Captain about running the QRH for the Fuel Leak and he said 'I'm not gonna do that because it leads you to shutting down the engine; etc etc.' He then also said something along the lines of 'we have enough fuel to continue back to ZZZ. That procedure is more for if you're over the water on a longer flight. I'll just keep the left fuel pumps off and the crossfeed open.' I then made the comment 'I wonder where the fuel is going?' to the Captain. I didn't think of it at the time; but I definitely should have spoken up more about the fuel pumps configuration and running the Fuel Leak QRH procedure. Once our duties were complete; the Captain and I came back together. I brought him into the loop by telling him we were a priority aircraft; all set up for Runway XXC and all I had to do was brief the approach. The Captain resumed his pilot monitoring role. ATC then asked how the fuel leak was going (rate of leak) and if we had it contained/under control. The Captain replied by saying 'we did some trouble shooting and we cannot get it to stop leaking.' I remember thinking to myself 'what trouble shooting?' When ATC asked about the rate of the leak the Captain told them 100lbs per hour. I then told him he should correct it to be over 500lbs in under 10min. I mentioned to the Captain I noted the time when I [advised ATC] (XA:30) and the fuel was 7.7x and the time was now XB:38 and we had 7.4x in that tank (300lbs in 8 minutes). Shortly after that; I glanced at the QRH and made the comment 'you're right. It does have you shut down the engine in the QRH. Interesting.' This was my second attempt at inquiring about the Captain running the Fuel Leak QRH. I could have been more assertive in asking the Captain to run the QRH procedure. I also noticed the procedure called to turn on all the main fuel pumps and close the crossfeed. The Captain did say he would turn on the left main fuel pumps and close the crossfeed for landing. He configured the fuel panel on final approach. Let me be clear....the QRH procedure for a Fuel Leak or Fuel Imbalance was never completed. We then completed a precautionary; under weight landing. We stopped on the Runway; put the flaps to 40 and got inspected by ARFF (Airport Rescue and Firefighting). ARFF inspected the aircraft; and did not note a fuel leak. We shut the left engine down and taxied to the gate using only the righthand engine. I noticed the leak appeared to stop during taxi in after we shut down the engine. I don't recall mentioning this observation to the Captain. It wasn't until after the fact when I looked back at the QRH procedure for curiosity that I saw the note about 'shutting down the engine to stop the leak.' ARFF followed us to the gate. Upon arrival at the gate; Maintenance did not see any visible fuel leaking on the exterior of the aircraft and also made the comment 'I wonder where the fuel is going because I don't see anything outside.' I remember noting the fuel at the gate after all was said and done read around 12;400lbs. The left fuel tank still showed significantly lower than the right fuel tank. The time from takeoff (18;xxx+lbs) to landing (12;400lbs) was under 1 hour total time. The Captain and I then debriefed the event. I mentioned I could have landed flaps 40 so I didn't have to move the flaps from 30 to 40 once stopped on the Runway; he could have made the remain seated PA after stopping on the Runway and I again expressed concern about how he did not run the Fuel Leak QRH. I did agree with him that we had enough gas to make it back to ZZZ safely - which we did. The Captain used prior experience and judgement to 'troubleshoot' an abnormal. I used muddled speech instead of assertion to get him to run the QRH procedure. Even though I was curious where the fuel was going; I didn't speak up to say the fuel could be leaking into the engine pylon etc. and cause us to have more of an abnormality.