It needs to be able to withstand a variety of gravitational strengths
Use what seems appropriate for each situation. You want very different architectures for high and low gravity, the atmospheric composition and pressure above the roof, the local radiation and meteor hazard, etc etc. Under lunar gravity, you can make use of heavy but potentially common and cheap materials like steel as structural components, but with more Earthlike gravity you will need more exotic structures, alloys and fancy carbon-nanotube-based materials if you want huge domes with widely spaced supports. Transparent hydrocarbon polymers might work if the local star is distant or cool, but UV damage might be a problem on other worlds, etc.
Roofs which merely have to separate an external from an internal atmosphere with a similar ambient pressure have quite different design constraints than those which have to separate atmosphere from vacuum. The list of circumstances isn't quite endless, but there are a lot of different planetary environments you might be able to build these things in.
You'll also have to deal with local material availability. For example, carbon, silicon and oxygen are widely available in the universe, giving the possibility of diamond or quartz windows, but sodium is rather more rare so normal glass is less likely to be available (which is a shame, because it is nice and clear and is a good UV blocker).
to reflect most forms of damaging radiation and stellar winds
One does not reflect either with matter. For EM radiation (generally UV) you just need to stick enough mass in the way to prevent the contents of your worldhouse getting fried, and that depends on how much UV your star is emitting (very little for a red star, quite a lot for blue stars),l how far away the planet is from it, and how UV sensitive its occupants are.
Charged particle radiation, such as solar wind but also more hazardous things like solar proton events or galactic cosmic rays, can sometimes be deflected with a suitably clever arrangement of magnetic fields, but no matter how hard you try some of those particles are going to hit the ground. It may be possible to suspend a cloud of charged particles above the roof as a sort of plasma shield, but this is veering off towards quite theoretical kinds of engineering which I know too little about to talk about here.
Your best bet is mass, and as much of it as possible, though that can be rather hard to arrange on an airless world if you want a transparent roof. This problem was worked around in the Stanford Torus space station proposal found in appendix K of Space Settlements: A Design Study, using "chevron mirrors":
This shows the action of the chevron mirrors in allowing light through shielding, by bouncing it three times off reflective surfaces, but blocking direct transmission by any radiation that can't undergo specular reflection from the mirrors... that would include charged and neutral particle radiation, and short wavelength EM such as vacuum ultraviolet and x-rays and so on.
It would be tricky to keep this nice and lightweight for large expanses of unsupported roof, but with enough pillars and suspension structures it might be made to work. It might also spoil the view slightly, so no uninterrupted vast expanses of clear glass for you.
and to be strong enough that meteor impacts don’t damage it.
Problem is that on airless worlds, meteorites are going to be coming in at escape velocity. On the Moon that's 2.4 km/s, faster than supersonic antitank rounds, and on the Earth it is over 11 km/s and there's no armor in existence that can shrug off that sort of impact.
Your best bet is to make the roof out of multiple layers materials, widely spaced, somewhat like a Whipple shield. Accept that it is going to get damaged by small impacts, and be prepared to continuously repair it. To defend against larger impactors you need a serious "space guard" program with powerful and highly capable multispectral telescope and radar arrays and a range of interception equipment to deflect or vaporize problematic debris before it reaches the surface.
In any case, you'll almost certainly want to have undergound emergency shelters readily available throughout the worldhouse, and ideally have the ability to partition very large 'houses so that a big puncture doesn't strip the atmosphere from a country-sized region, but maybe only a city-sized one. You might also want to consider the threat of deliberate damage to the roof... sabotage of active support and repair systems, or use of weapons.
Partial worldhouses are supported by single pillars at the centre
I'd say that very much depends on the gravity and atmosphere of the world you're building on. Designs must adapt. There's no one-size-fits-all here!
Using air pressure to partially or wholly support the roof is great if you can do it, but this needs to be offset against the risk of puncture.
