A B757-200 flight diverted to a nearby airport upon identifying a significant fuel leak.

Narrative

I was the pilot flying. We had done a lot of deviating around weather the first two hours. Approximately 2:15 into the flight; we received a Fuel Disagree FMC message. At that time there was a 4000 pound difference between Calculated and Totalizer fuels. There was also a 300 pound imbalance between the main wing fuel tanks (right wing down). This was about 15/20 minutes after the center tank fuel pumps were shut off. We ran the Fuel Leak checklist in the AOM. Per the checklist; we started the Captain's clock for 30 minutes and had the Flight Attendants look for a Fuel Leak on the right engine. They reported no abnormal conditions. After 30 minutes our imbalance between main wing tanks increased to 1200 pounds. This equaled a 900 pound increase in fuel imbalance occurring in 30 minutes. At that point; we set up a phone patch with Dispatch and Maintenance Control. We all agreed we had a fuel leak on the right engine. A divert to ZZZ was the best option. Maintenance Control agreed we should shut down the right engine per the Fuel Leak checklist. We declared an emergency as a precaution and performed a single engine landing with flaps 20 per the checklist.