Are metric measurements all derived from the value 1kg? If so, does this mean that the entire metric weight range can now be officially based on mathematics?
No, at least second and meter are defined with math and elementary physics (e.g. second is the time it takes for a specific atom to oscilate a specific number of times).
Wouldn't that change though based upon the isotopes of the atoms in it? For example H2O made with Deuterium (1 proton 1 neutron and 1 electron) or Tritium (1 proton 2 neutrons and one electron) vs Protium (1 proton 1 neutrons and 1 electron), could all give different weights, not to mention different isotopes of oxygen 16 17 and 18 for the most common/long lived.
In a (much more rational than SI) system "h=c=1" there is only one fundamental unit left - kg (or ev, which still depend on a kg definition). So getting rid of kilogram is absolutely essential.
That system is mostly irrelevant for cultural and legal purposes. Even in the specific philosophical framework where getting rid of the kilogram 'absolutely essential', the current importance of the kilogram would simply migrate to the importance of the specific conversion factor to traditional units.
Of these, mole and kilogram are dependent of the kilogram.
edit: this is a good, if maybe a bit misleading, illustration: http://www.nist.gov/pml/wmd/metric/upload/SI_Diagram_Color_A...
[1]: http://www.nist.gov/pml/wmd/metric/si-units.cfm