CLR profiler does not seem to work with the Silverlight CLR. Does another memory profiler exist?
VS2010/SL4 has a profiler now checkout:
http://www.nachmore.com/2010/profiling-silverlight-4-with-visual-studio-2010/
http://blogs.msdn.com/b/seema/archive/2010/01/28/pdc-vs2010-profiling-silverlight-4.aspx
Standalone CLR profiler has been updated to work with Silverlight so you don't need to have VS Premium/Ultimate.
David Broman's CLR Profiling API Blog: CLRProfiler V4 Released
UI isn't that great, but it works.
I use free XTE Profiler which also works with Silverlight Standard and Out of Browser applications. Shows live memory usage as well.
Try using Atologic SilverProfiler. Available at www.atologic.com.
Doesn't seem to be one available yet. However, as recommended in this forum thread, you can convert your Silverlight app to a WPF application and profile that:
There is no tool as of now but as a workaround you can easily create a desktop (WPF) version of your Silverlight client from the same code base and few tweaks (refer Scot's blog for an example on this - http://weblogs.asp.net/scottgu/pages/silverlight-tutorial-part-8-creating-a-digg-desktop-application-using-wpf.aspx) . Once you are done with this you can run any performance profiler that works with WPF.
Not an optimal solution, but it sounds like the best option for now...
Update: Just saw a blog post about XPerf which is a cpu sampler for Silverlight. Not exactly a memory profiler but a good tool for testing the performance of Silverlight apps...
Though not a full blown profiler with a yummy GUI, you could use Windbg + SOS to debug your silverlight app, it would require a lot of manual work, but you can then walk your managed heap.