BEA Weblogic Question:

No. Within an unsigned applet, you cannot load native libraries over the wire, access the local file system, or connect to any host except the host from which you loaded the applet. The applet security manager enforces these restrictions on applets as protection against applets being able to do unsavory things to unsuspecting users.
If you are trying to use jDriver for Oracle from an applet, then you are violating the first restriction. Your applet will fail when it attempts to load the native (non-Java layer) library that allows jDriver for Oracle to make calls into the non-Java Oracle client libraries. If you look at the exception that is generated, you will see that your applet fails in java.lang.System.loadLibrary, because the security manager determined that you were attempting to load a local library and halted the applet.
You can, however, use the WebLogic JTS or Pool driver for JDBC connectivity in applets. When you use one of these WebLogic multitier JDBC drivers, you need one copy of WebLogic jDriver for Oracle (or any other two-tier JDBC driver) for the connection between the WebLogic Server and the DBMS.