Fuel weight is a pretty minor factor. A 33-gallon tank vs. 19-gallon, that's 14 gallons at aprx. 7 lbs/gallon, so about 100 lb. Not a major player compared to your utility box and its contents. And the weight of the fuel in the front tank is in great part on the rear axle anyway. The thing you lose going single-tank is the insurance/backup factor of a second tank. Take your sitch right now, for instance. You could drop the tank with the bad sender, and if it takes several days to find a replacement, or find the time to finish the job, or you decide to prime/paint the tank, etc., you can continue to run the truck on the other tank. Single-tank truck is DOWN for the duration. And if you fill them alternately, just in case you get bad fuel one day, you won't be grounded by bad fuel in both tanks.
IIRC, the F250s could be ordered with one more leaf, basically the same spring as in an F350, just not the same block. ***MIGHT*** be enough to help with that squat.