Using a rock and an aeroplane would be a better example. A paper aeroplane weight less than a rock. A paper aeroplane will be blown about in windy conditions, a rock will not (Unless it's REALLY windy),
I don't think it's a *better* example. In fact, I find the example worse.
A rock and a paper aeroplane on the ground will be blown about, or not, because the forces exerted by the wind are higher than the friction between the object and the ground, or not. The rock is denser so will experience less aerodynamic force and more friction, so it takes a higher wind to blow it about.
And a rock and a paper aeroplane that are free-falling will be blown about by the wind equally. However, it takes a while before the wind has overcome their momentum fully, and before that happens the rock will be on the ground. So it might appear that a rock will fall straight down, even in the wind, but that's just because it takes a while for the wind to "catch" it.
And that momentum is the key. Assuming steady conditions (non-gusting x-winds for instance), the weight, size and shape of the aircraft don't matter one bit. But if you assume non-steady (gusting) conditions, it becomes a matter of the actual weight of the aircraft and it's size. Or better yet, it's aerodynamic shape as seen from various angles.