Connectivity to any database is accomplished through JDBC drivers; it has nothing to do with WebLogic. If I recall correctly, WebLogic ships with drivers for Oracle, Sybase, and perhaps SQL Server, but you have to add any others that you need.
This is true of all Java EE app servers, commercial or open source.
The value that WebLogic adds is JNDI services and connection pooling. It allows to configure pools so that connections are checked before users are allowed to use them, stale connections are recycled, etc. These are features that would be laborious to code on your own. WebLogic makes it easy to do via configuration.