■ The routing for the flight was unusually long.... I had additional fuel added for the re-route. About an hour before landing, we were given a 45 minute hold about 180 miles south of [our destination]. Thirty minutes into the hold, I declared minimum fuel. We were cleared to exit holding and proceed on the arrival. After a few more minutes, ATC informed us that [our destination] was not taking any arrivals. We asked about our alternate…and were told that it was unavailable. We advised that we had a fuel emergency and were given a heading for [a third field]. When we started the turn, we were told that [our destination] would now take us. We continued and had sufficient fuel to get there with enough for Reserve and Alternate.

To my surprise we burned additional fuel that put us below Reserve and Alternate requirements. The First Officer was Pilot Flying and we were cleared for the ILS…. TRACON dropped us off a bit high and close on the approach. The First Officer armed Approach but the aircraft didn’t capture since we were capturing the glideslope from above. The aircraft leveled off and very quickly went from 1/2 to 2 dots high. We were in IMC at 2,000 feet. The First Officer turned off the autopilot and continued the descent. I put the Flight Director into Vertical Speed mode but we ended up about 1 dot high at 1,000 feet. The First Officer said, “Not stable.”

■ We noticed approximately 1,000 pounds of fuel imbalance passing FL180, but decided to wait until level off to address the issue. Level at FL370, we noticed that the right tank was 3,000 pounds heavier than the left. We checked the fuel used and the total fuel indications on the FMC (Flight Management Computer). As best we could tell, our level off fuel was approximately 3,000 pounds less than planned.

■ We were cleared for the visual to 22L. We were also told to maintain 180 knots until 5 miles out. The First Officer extended the final approach course from the Final Approach Fix (FAF). The Approach checklist was already completed. I noticed we were going to intercept the final approach well inside the FAF. I called for the First Officer to set 1,500 feet on the Mode Control Panel (MCP). The FAF altitude was 1,700 feet. I clicked the autopilot off and armed Approach mode. I also had Level Change and Heading Select at 270 set on the MCP…. At approximately 8 miles I called for Gear down, Flaps 15, set 180 knots. Approaching final I noticed the airspeed was at 180. The VASI appeared and was showing red over white, on path. I called for 160 knots and then called for Flaps 30. At approximately 1,200 feet AGL, the First Officer said the flaps were indicating 25. I checked the handle and it was at 25. I asked him if he had set 30 and he said yes, but they stayed at 25 so he had returned the handle to 25…. I waited to slow to about 160 knots and called for him to set 30. The flaps did not move from 25. We were now at about 600 feet AGL. Weather was clear; dry runway; approximately 9,000 feet of available runway.

■ Inside the Final Approach Fix we encountered a Windshear caution. We were fully configured and the airspeed varied from plus 20 to minus 10 knots. The event lasted maybe 10 seconds. Just under 1,000 feet AGL, the aircraft popped well above glide path with a High Speed aural warning. The radar was painting severe weather on the opposite side of the airport.

■ Shortly after level off at FL380, we selected Airborne Weather Radar “On,” since convective weather was forecast along our route. “WX FAIL” appeared on the Navigation Display and no weather radar returns were present, indicating a failure of the Airborne Weather Radar system. We consulted the QRH, Operations and Aircraft Manuals and the Minimum Equipment List. None offered guidance for this failure.

■ I said, “Continue.” Our fuel state was now about 400 pounds below Reserve and Alternate. I had some ground contact also at 1,000 feet. I knowingly violated Standard Operating Procedure (stable by 1,000 feet) because I did not want to go around and end up in a worse predicament. I felt we were both fatigued and we were getting low on fuel.

■ We referred to the irregular procedures for the “Fuel Configuration” light and decided against attempting to balance the fuel due to the uncertainty of the cause of the imbalance (possible fuel leak in the left tank). The fuel indication in the right tank appeared to be stuck. We verified the right wing heavy by hand flying the aircraft and using rudder trim to level the wings. Trim required increased from 2.0 units to 4.0 units as the flight progressed. We were unable to determine if the fuel in the right wing was trapped and unusable. We decided to return to [departure airport] since it was only 60 miles behind us and the weather was clear.

■ I decided to continue the approach and landing after concurrence from the First Officer. Vref was recalculated at 146 knots with a target speed of 152. The calculated stopping distance with Auto Brakes 3 was approximately 6,600 feet at our weight.

■ I had full visual of the runway at all times and determined that the safest plan of action was to get the aircraft on the ground. The severity of the line of weather ahead would have been much more hazardous than the unstable approach…. This experience will have me going to an alternate before this happens again.

■ We asked Center if there were any other [Company] aircraft in the area headed to ZZZ that we could follow. Center vectored us into 20 mile trail of [Company Flight #]. We established communication with the flight using our secondary radio. He then led us safely to ZZZ, deviating around weather when necessary.