Will optimising the weight distribution of a commercial flight save fuel?
For precisely this reason the A310-300 had a fuel tank in the horizontal tail. However, the pilots I spoke with (Pan Am) did not understand the purpose and insisted that the tank is empty all the time. The A330 and A340 also have a tail fuel tank, and here its fuel level is automatically controlled.



A330 tank arrangement (picture source). Note the trim tank in the horizontal tail.

Shifting the c.g. a little back reduces drag slightly (less than 2% reduction in fuel consumption, depending on initial c.g. position) but also static stability. This is no problem when the FCS adds enough stability, but in case of a system failure you should make sure that the rear tank can be emptied soon. Hand flying an aircraft with relaxed static stability is tiring.

The A350 did away with this feature because it was felt that the added complexity would outweigh the benefits.