The old saying goes, nature abhors a vacuum, but that isn't exactly true. The universe is full of vacuum; what nature abhors large energy differentials.
So for example, a vacuum chamber has to be strong enough to withstand the ~101kPa of pressure on the surface, and typically the materials required to build such a structure are heavier than the volume that contain.
I've often heard references to Neal Stephenson's Diamond Age, and people saying that perhaps one day we'll be able to manufacture small strong nano structures that are lighter than air (indeed, it's quite plausible: http://www.euronews.com/2012/11/01/lighter-than-air-material-discovered/).
However, I'm curious why concentric partially pressured spheres wouldn't work as an approach.
If you consider a structure which is in cross-section:
Outside | P1 | P2 | P3 | ... PZ ... | P3 | P2 | P1 | Outside
Where the value of P(n) is something like, say, P(n-1) * 4 / 5 (or some other fractional amount), and PZ ~= 0, it seems to me there's no reason why it wouldn't be possible to build the structure out of relatively light, relatively weak materials with many concentric layers that wouldn't collapse.
Perhaps there would be some minimum gap distance required and there are also practical considerations like, 'what stops the spheres from falling due to gravity and touching; when two surfaces touch the pressure difference is effectively the delta over the two open spaces; which will eventually be external vs. internal vaccum and break the structure', 'how would you depressurize the spheres', etc.
...but lets say for an ideal situation in which the structure floats in a gas without a strong gravity source to mess things up, and the pressure has been magically set in advance in each pressure zone.
Does this work?
If not, why does the structure collapse?
Could it be possible to actually fabricate such a structure?
(for example, a single pipeline running from the edge to the center could maintain the position of the spheres and depressurize them one at a time as required; the amount of material to do this (despite being dense) would be related to the radius of the sphere, while the buoyancy would be related to the volume of the sphere. Plausibly a net positive lift could be generated, I imagine...)