B767-300ER First Officer reported while correcting a fuel imbalance issue; fuel quantity was noticeably low resulted in expeditious handling requiring a divert.

Narrative

During cruise over the Pacific; and in ETOPS; the (PF) Relief CA (R-CA) and myself the (PM) Relief FO (R-FO) had gotten the redispatch message 2 hours prior to our redispatch point. The CA and FO were at rest. We (R-CA & R-FO) noticed that our calculated fuel was just barely above our min-fuel required to continue to ZZZZ1; and totalizer fuel was below the min-fuel required. The difference between calculated and totalizer was hovering around 1;000lbs difference; which we thought was normal but; we inquired with dispatch to be sure of our min fuel. While dispatch was working on the issue; we had a fuel config EICAS message. This is not unusual; especially on long flights; and both of us looked at the totalizer and noticed an imbalance. We opened the QRH to 12.1 to proceed through the checklist to crossfeed and balance the tanks. During the crossfeed operation; I (R-FO) noticed the right main tank lost 2;500 lbs of fuel in approximately 60 seconds. The difference between calculated and totalizer was now 3;500 lbs. We both quickly agreed to turn on the left main fuel pumps and finish the QRH and stop the crossfeed operation immediately. This seemed to have stopped the fuel leak. We woke up the resting crew and got them in the observer seats. At this point dispatch had sent a new message that might have been accepted; however we no longer had the fuel to continue. We called dispatch via sat-phone and started a three way call with maintenance control. Explaining what had happened; maintenance advised it's possible that the fuel could have been spilled overboard due to a faulty valve(s); but there is no way to know without trying again. Everyone agreed we no longer had enough fuel to continue. After conferring with dispatch; Maintenance Control; a duty pilot and the fleet captain; all parties agreed with concurrence that the safest course of action was to divert to ZZZZ. Dispatch sent routing to ZZZ1 for us to request with ZZZ scheduled Day Off. We called ZZZ on HF and requested priority handling with a possible fuel leak; and advised that we believed we were no longer leaking fuel but couldn't continue to ZZZZ1. We quickly received the route clearance from ZZZ; the R-CA and R-FO successfully diverted the airplane towards ZZZZ. At this point we had time and swapped crew. The CA and FO were back their respective seats and fully briefed. Over an hour after we had diverted the right main tank indications went blank for several minutes at a time. This had not happened before the crossfeed fuel leak issue and only started over an hour after diverting. One the indications returned; the fuel readings still showed a discrepancy of 3;500lbs between calculated and totalizer. We continued to ZZZZ where we made an uneventful landing ~3 hours after the initial issue. All crew members performed very well in a high-stress situation; over water with a possible fuel leak; 1;000 miles from the nearest runway.Cause: During a crossfeed operation while following QRH 12.1 for FUEL CONFIG EICAS message; the right main tank lost 2;500lbs of fuel in approximately 60 seconds. We quickly stopped the operation; and showed a discrepancy of 3;500 lbs between totalizer and calculated; with totalizer being the lower of the two. We noticed that the rate at which we lost fuel was coincidentally about the same rate as jettison (2600 lbs/min). With no fuel in the center tank; however; this seemed very odd. Maintenance confirmed it might still be possible; but the actual reason is still unknown. The totalizer fuel did seem to decrease properly as we burned fuel on the way to ZZZZ. The discrepancy remained at 3;500lbs all the way until landing. Our estimated fuel upon arrival (using the totalizer) was spot-on when we arrived at the gate.Suggestions: Without a clear cause for how fuel could be spilled overboard from the main tanks; this issue may require extensive Maintenance troubleshooting.