What is difference between TOMCAT server and BEA WEBLOGIC server
Tomcat is a Servlet/JSP container. It is free. It does not support the Java EE 6 container features such as EJB/JPA out of the box. These can be integrated but will not be equivalent to a proper EJB container.
WebLogic Server is a fully loaded EJB container. It has the best server and database connection pooling features in the market. It is easy to build/deploy/debug apps on Weblogic. It's a commercial product and quite expensive at that.
Apache Tomcat is an open sources Servlet/JSP container (it was the Reference Implementation for the Servlet/JSP APIs prior to Servlet 2.5/JSP 2.1), it does not implement the whole Java EE stack (no EJB container, no JTA, no JMS, etc). Tomcat "competes" with Jetty and Resin but is not comparable with a Java EE certified server.
BEAOracle WebLogic Server is a commercial Java EE application server that implements the whole Java EE specification. It is known to be a mature, extremely stable, secure, performant application server and is used in many "mission critical" applications. In short, it's the Rolls-Royce of application servers. But it's expensive too. WebLogic competitors are WebSphere (commercial), JBoss, GlassFish, Geronimo, Jonas (open source).