How are Virgin Galactic's SpaceShipTwo's windows so large?
Here are a few ideas:


First and foremost, we're not handling metals here. Composites have the advantage of being able to be made stronger by adding on a few layers around high-stress area like windows. This was difficult with metals since this needed some sort of fasteners or adhesives to do. This reinforcement is seen in the photo below.
The windows are designed to keep an even pressure all around in the context of the fuselage shape at that point. You'll notice the flange design which keeps the fuselage shape and stop it from popping open. This is a little like the thicker part of a bottle neck. This is very difficult (if possible) to do well in a metal fuselage to this extent.



(source: msn.com)  


The usage is completely different. Concorde was a commercial aircraft, intended for many years of operation. This is a very low-cycle aircraft which will see a fraction of that flying. The number of pressurisation cycles is a lot lower, putting much less force on the windows. 
As for safety, the style of flying is completely different. Probably flown by test pilots, the aircraft might never even experience rain and will fly under very predictable conditions, with very few flight cycles. 
Periods of elevated temperatures gradually degrades many materials, this is much less a concern with short flights. If I gather correctly this is the main issue with sustained high-speed flight, as seen on Concorde and SR-71 and other aircraft.



(source: guardian.co.uk)  


Composites have a lot lower thermal expansion (CFRP vs. Aluminium is an order of magnitude lower) which reduces issues with expansion in the fuselage.
Concorde was a commercial aircraft with weight and operating price in mind. This aircraft is built for this purpose, with the windows considered as a main feature from the start. You could probably have been able to make the windows a lot larger on Concorde, at the unacceptable price of weight, production and operating cost.
Needless to say that knowledge of materials and structures has advanced substantially, all our these features can be modelled in detail on computers, not necessitating the traditional conservative approach.
As for redundancy, predecessor SpaceShipOne had double pane windows and double seals everywhere. For the passengers without suits, if a window were to blow entirely, you're most probably out of luck.