General considerations:

https://timtaubert.de/blog/2014/10/deploying-tls-the-hard-way/

To check current SSL/TLS version and cipher suite used for SSL connections:

$ openssl s_client -connect hostname:8888

example output:

New, TLSv1/SSLv3, Cipher is AES128-SHA
Server public key is 2048 bit
Secure Renegotiation IS supported
Compression: NONE
Expansion: NONE
SSL-Session:
    Protocol  : TLSv1
    Cipher    : AES128-SHA
    Session-ID: 5523B18F98C687FD8E76527F827E86EA47C603C8D105DF1D5428468A83ACA7D5
    Session-ID-ctx:
    Master-Key: 7C2824A28A3722A8072082D6CB69ED3C2D6DA669B7D46E4FC994AFB71150B324A0D55E59569377FF9C93A8DF0DE80BE1
    Key-Arg   : None
    Krb5 Principal: None
    Start Time: 1428402575
    Timeout   : 300 (sec)
    Verify return code: 0 (ok)

Set TLS version for WebLogic:

-Dweblogic.security.SSL.protocolVersion=TLS1

Set ciphersuite (in $WLS_DOMAIN/config/config.xml):

  <server>
    <name>ServerName</name>
    <ssl>
      <enabled>false</enabled>
      <ciphersuite>TLS_RSA_WITH_AES_128_CBC_SHA</ciphersuite>
      <jsse-enabled>true</jsse-enabled>
    </ssl>
    <machine>host1</machine>

....

List of Ciphersuites Supported by Weblogic Server are:

Cipher Suite Symmetric Key Strength
TLS_RSA_WITH_RC4_128_SHA 128
TLS_RSA_WITH_RC4_128_MD5 128
TLS_RSA_WITH_DES_CBC_SHA 56
TLS_RSA_EXPORT_WITH_RC4_40_MD5 40
TLS_RSA_EXPORT_WITH_DES40_CBC_SHA 40
TLS_RSA_WITH_3DES_EDE_CBC_SHA 112
TLS_RSA_WITH_NULL_SHA 0
TLS_RSA_WITH_NULL_MD5 0
TLS_RSA_EXPORT1024_WITH_DES_CBC_SHA 56
TLS_RSA_EXPORT1024_WITH_RC4_56_SHA 56
TLS_RSA_WITH_AES_128_CBC_SHA 128
TLS_RSA_WITH_AES_256_CBC_SHA 256

In the past AES_256 did not work until we download the unlimited jurisdiction jars from SUN.

Download JCE_policy_1.5_0.zip
Place it in /JRE/lib/Security/
Also Replace localpolicy.jar & US_Export_Policy.jar