Which Weld version are you using?
We fixed some related issue in 1.1.2.Final.
<dependency org="org.jboss.weld.servlet" name="weld-servlet" rev="1.1.2.Final" />
<dependency org="org.jboss.weld.servlet" name="weld-tomcat-support" rev="1.0.1.Final" />
The above is the latest weld-tomcat-support.jar I could find.
The error message is related to AnnotationProcessor which has been dropped from Tomcat 7.0, as I understand.
It seems Weld supports Tomcat 7 supports Weld Servlet Injection out of the box, without any configuration, so sorry for the unnecessary post.
Now I am getting an error about inactive conversation scope, but this is unrelated, I think.