FYI: Just created the first bug report regarding the Java SE + weld + jersey problem with attached project that shows how to reproduce :-)
Still need to work on reproducing the Java EE + weld + jersey problem for you.
P.S hope you do not feel that I am too aggresive in describing the 95% of Jersey I love and the 5% "feature" I really, really don't like :-)... Just to be clear, I feel Jersey is a VERY good project and you guys are doing a great job. But with great work comes great responsibility and expectations :-)
Cheers,
Morten