My perspective about using silverlight for developing a web App is, It helps in developing rich, interactive web application for internal (LOB) applications and public facing internet websites. It vastly reduces the development, testing, maintenance, and support effort required to deliver a successful business application. It provides many of the rich capabilities of desktop applications (e.g. drag-and-drop, animation, fast video streaming and other interactive abilities).
Some of the other benefits are:
Easy to design app with rich graphic, animation,etc.
Fast and light weight.
Out of browser capability.
Takes advantages of client hardware configuration, etc.
Hope this answer is helpful.