I believe this idea is flawed. While it is possible to raise a heavy weight with very low air pressure, it's possible to use heat at a low temperature to accomplish this, and it's possible to do it fairly efficiently, the problem lies in the losses encountered while cycling this kind of engine. I'm not referring merely to frictional losses, although that is a serious problem also. Consider the system: A large green house is used to heat a large volume of air. Some of this air is sent to the expander to raise the weight. So, we've just removed some mass of air from the greenhouse. Now, the "engine" cycles as the weight rotates it. However, we have to raise the weight again to get a continual output. So, the air that was placed in the expander has to be removed. You can't just send it back to the greenhouse because it's under pressure and doing so would consume all the mechanical energy we just produced. So, the only other option is to expel it from the system. So, now we start another cycle while venting the opposite side of the cylinder (to expel the previous charge as discussed). Now we have removed yet more mass of air from the greenhouse! The only way to affect a continual rise in pressure is to continue raising the temperature of the air indefinitely, and this is not possible. There has to be a means to replace the mass lost from the greenhouse, and this can't be done without expending precious mechanical energy! The only other way is to allow the air contained in the greenhouse to be cooled to lower the pressure within and allow a fresh charge of outside air at atmospheric pressure to be drawn within. However, that means we lose most of the heat energy that has been collected! The net effect is a system of pitifully low efficiency, and considering the extreme frictional losses of a very large machine, the net efficiency would almost certainly be so low as to be totally impractical.
I am certainly willing to hear an explanation as to how my reasoning here flawed. After all, it would be great if the thing works... but I know better.
A better solution is to use the density differences caused by heating air to induce a differential pressure to cause air flow. This air flow is used to power a turbine. The efficiency is low, but the system is practical because no pressure vessel is required. An interesting aspect of this system is that it continues to produce power for many hours after nightfall due to the residual heat in the system:
http://www.youtube.com/watch?v=XCGVTYtJEFk&feature=related
http://www.gizmag.com/enviromission-solar-tower-arizona-clean-energy-renewable/19287/