In Aussie you can fly what you like regardless of weight on a PPL, just undertake the flight training relevant to the aircraft type.
If you want an ATPL then do the appropriate course; if you want an abbreviated CPL or ATPL there are ways around the previous minimums by doing MCL and all the sim.
If you don't want an ATPL because you fly privately then just fly privately. An ATPL requires a MCL and a two crew check to be issued with an ATPL, that's all.
I can't fathom why a regulator would try and stop a PPL from flying a heavier than 12,500 lb aircraft