Star Trek: The Next Generation (TV series): Why did they change the uniforms between Season 1 and 2?

The original uniforms were basically swimming suit spandex turned inside out (so the rough "inner" side was outside" and, unfortunately, turned sideways.The thing about that material is that it's only really vertically stretchy.  It has some horizontal give, but not nearly as much as it would need.They did this in order to make it look more like fabric and less like spandex.  In the picture you provided as an example, for instance, you can see Picard's sleeve bunching up and draping over his arm in a way that spandex typically wouldn't.  The downside is that this meant that the uniforms were providing constant compression on their torsos.  Combine that with the natural tendency of the jumpsuit to bunch up when they sat down (which it did most of the time) and something had to give.That "something" ended Sir Patrick Stewart's back.  A friend of mine actually knew an osteopath who examined him after the end of the second season.  Apparently the gist of their conclusion was that if they wanted their star to still be able to walk they needed to ditch the uniforms NOW.

During season 2, Brent Spiner was actually wearing a back brace under the uniform, which if you look closely, can be seen. The original uniforms couldn’t hide the back brace at all.The original uniforms were not phased out. Only the guest stars got them in addition to mainline cast. All the extras still wore the original ones.