How has weight been reduced in commercial aircraft design and how will this trend continue?
Perhaps the biggest weight reduction in aircraft across the board has been the use of composite materials over aluminum. This extends from small GA aircraft all the way up through airliners like Boeing Dreamliner. In the retro fit game, some older planes have been certified to take newer composite propellers. Even small savings matter according to this article 


  LED modules give on average a 40% weight saving over the incandescent
  modules they are replacing, which improves fuel economy


Glass cockpits and modern computerized avionics tend to weigh less and offer more than their earlier steam gauge counter parts. Even in the space shuttle.  


  The system also provides greater backup capability, weighs less and
  uses less power than the original design.


Another thing that has made a fair dent in take off weight is how fuel efficient engines have gotten. While there is a practical limit to this as engines have gotten more efficient the need to carry fuel has dropped or planes can go farther on the same fuel. In a similar vein as weather planning/predicting has gotten better fuel loads (while still in compliance with FAA reserve regulations) may be slightly lighter as they can now be more precisely calculated. 

The one thing that has gotten heaver is the passengers...