It takes up less room in the rocket, and weights a lot less. The internal air pressure gives it its shape; instead of fighting with air pressure, puts it to use. The skin is in tension, so it can have great strength to weight ratio. It's not just a thin layer, but thick enough to resist space debris and micrometeorites as well as the rest of the ISS; it is strong enough that it might make a neat yurt back on earth.

When they started inflating it on the first try, it didn't open properly; evidently the material was sticking together. According to Bigelow's press release:

The BEAM spacecraft has been in a packed state for a significantly longer time than expected. It has undergone a tremendous squeeze for over 15 months, which is 10 months longer than planned. Therefore, there is a potential for the behavior of the materials that make up the outside of the spacecraft to act differently than expected.