Recommended Best Practices for Securing WebLogic Server.

Disable SSL V2, Weak Ciphers, and Null Encryptions

You can use the following jvm options to disable Weak Ciphers.

Steps to disable SSL V2 follows later.

Use Secure Cookies to Prevent Session Stealing

Please refer to this article : link

Configure WebLogic Server to use a Specific Cipher Suite or a List of Ciphers

Please refer to this article : link,TLS_RSA_WITH_RC4_128_MD5

Restrict the SSL Protocol Versions Allowed by WebLogic Server

Please refer to this article : link

You should also allow only the required http methods ( GET/POST) to access the resource on the server. You can restrict other methods from the web.xml

Refer this