Well, the Saturn V/Apollo vehicle was 2800 tonnes at liftoff, so it probably depends on how you define "heavier-than-air aircraft".
The SV didn't have wings - but then, it didn't need wings.
There are ways around the cube-square law, because that only really applies to solid objects - vehicles are mostly "hollow", which is why an iron ship can float, but a solid chunk of iron sinks.
Birds have hollow bones, but are still mostly "meat" by volume, thus a bird as big as an An-225 is impossible - but the An-225 itself flies just fine.
I'm sure that, given an infinite airspace (depth and breadth) there is probably some point where the aerodynamic equations may start to warp or break down. I'm also sure that such limits are comically large compared to a simple problem such as - what happens if your two wing tips are in different weather systems?
My bet is that there is no theoretical reason why a 10000-tonne aircraft could not fly. It would be an expensive and difficult engineering problem (but that is technology, not theory).