Transformer can only do so much. Then the core saturates. When you load it beyond that point, its voltage will go down. Meanwhile battery voltage will go up because you're charging it. So they will become equal (minus two dide drops, which is far greater than 0.001V). If the transformer wire is not thick enough, it'll burn.
As the battery gets close to the full charge, the current will go down and the voltage will go up. For the 8V rated transformer, it might be as high as 10V (11V is the peak voltage for 8V RMS, minus diodes). If you apply such voltage to the 6V battery for a prolonged period of time, it'll boil out.