I have this idea. Sorry that I have to draw a circuit and have no other way to do it that this way-

This is an opamp amplifier in the non inverting configuration. Just do following additions to this circuit.
1) In place of Vin, connect the battery with a 240 Ohm resistor in series and with the sending unit connected in parallel to ground.
2) At Vout, connect the Weston meter to the battery via a resistor with value such that it allows only 50uA current when opamp output is 0V.
3) Choose R1 = R2.
Working:
When you tank is full, Sending unit has a resistance of 0. Therefore opamp output is 0 and the Weston meter will show a reading.
When tank is empty, Sending unit will show 240Ohm. Therefore opamp output is = battery voltage and Weston unit reads 0uA.
Since the design uses battery for everything and also expects Battery level voltage at opamp output, be sure to use a rail-to-rail opamp.
There is one thing to note here.
Quote:
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Typical fuel tank sending units have a resistance of 0 to 10 ohms in the full position and 90 to 240 ohms in the empty position
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This design doesn't take care of the high resistance inaccuracy of the Sending unit. I assumed 0 Ohm and 240 Ohm.
Hope this helps.

Karthik