Air carrier Captain reported a fuel leak and subsequent engine shut down during cruise. Flight diverted and landed safely.

Narrative

Prior to departure in ZZZ1 we had a fuel config light that would not stay illuminated. I wrote it up. It had been written up before and Maintenance changed the entire fuel panel to fix the fuel config light. This took a slight delay at the gate for Maintenance to fix this item. Fast forward to airborne cruise about 80 miles outside of ZZZ; I received a scratch pad FMC message that said fuel disagree. The difference was around 2000 lbs between the left and right value on progress page 2. A couple minutes prior I had turned the center tank pumps off; and at that moment I had verified that left and right tank were actually perfectly equal in quantity I transferred the flight controls to the First Officer (FO) and referenced the checklist which led me to the fuel leak checklist. I read the fuel leak checklist and was trying to determine if we indeed had a fuel leak or not. The right tank was dropping quantity very fast over 3000 pounds approaching 4000 in less than 10 minutes prior to this both left and right tanks were perfectly equal. I sent the First Officer back to look outside and he confirmed we had fuel spray off the right engine. I paused the checklist at the engine; shut down step and tried to contact Dispatch and Maintenance. Dispatch gave me a VHF frequency. I was unsuccessful in reaching Dispatch. I requested a second frequency and I still was unable to receive a transmission from Dispatch. I reverted back to text messages via ACARS; and I let Dispatch know we had a confirmed fuel leak; and we were going to shut down the right engine and we need an airport and I was requesting ZZZ that it was right in front of us and it was VFR. ZZZ2 was quite far away; and ZZZ2 was cat three at that time. I requested the weather from Air Traffic Control and I requested a lower altitude in preparation for engine shut down. I finished the checklist; calculated the landing distance; and I briefed the Flight Attendant. I made a PA and I requested priority handling with Air Traffic Control. Once the checklist was complete and the engine was secure. the fuel leak stopped. I reference the overweight; landing checklist in the diversion guide in the quick reference guide of the flight operations manual. I transferred the controls back to myself for the landing. We landed 2500 pounds overweight and the brake temperature were at four with two tires at five. I made a normal soft touchdown and had crash fire rescue inspect the aircraft on the runway. I had the First Officer make a remain seated PA; After receiving the OK from the equipment I made an announcement; expressing caring and safety; and that we will take care of each and every one of them and get them to their destination. I taxi the aircraft following an operations vehicle to the remote pack. Upon reaching the Pad; I spoke with Maintenance Control; Dispatch; and the Chief Pilot. I made additional announcements letting everyone know what was going on. It took a while for the stairs to arrive. The buses were only capable of carrying 17 persons and there was not any company personnel to assist us. I sent the FO on the first bus to have a representative in the terminal. I stayed with the aircraft and helped 17 or 18 passengers walk down the stairs and carried approximately 70 passengers luggage down the stairs because we did not have any anyone there to help us passengers were bus to the main terminal in small buses; this took an extensive time after all passengers were off. I stayed with the aircraft until the cargo was unloaded. I then shut down the aircraft and close the main cabin door ensuring the aircraft was chocked on all gears. I completed the maintenance write ups for overweight; landing; fuel leak and hot brakes.