The big problem is RAM. With 256 your way below our recommended and 256 below our minimum of 512Meg. This will cause lots of swapping. The CPU issue you see is from our process mon. Can you run top and vmstat 5 and report the output?
Can you tell which of the three Java processes seem to be eating CPU? I did a ps -ef on my test box and got back these two, but this is a slightly older version.
Code:
zimbra 2236 1 0 Sep16 ? 00:00:03 /opt/zimbra/java/bin/java -client -XX:NewRatio=2 -Xms1188m -Xmx1188m -Djava.library.path=/opt/zimbra/lib -Djava.endorsed.dirs=/opt/zimbra/tomcat/common/endorsed -classpath :/opt/zimbra/tomcat/bin/bootstrap.jar:/opt/zimbra/tomcat/bin/commons-logging-api.jar -Dcatalina.base=/opt/zimbra/tomcat -Dcatalina.home=/opt/zimbra/tomcat -Djava.io.tmpdir=/opt/zimbra/tomcat/temp org.apache.catalina.startup.Bootstrap start
zimbra 31102 31083 13 09:52 ? 00:00:00 /opt/zimbra/java/bin/java -client -Dzimbra.home=/opt/zimbra -cp /opt/zimbra/lib/zimbrastore.jar:/opt/zimbra/lib/commons-logging.jar:/opt/zimbra/lib/commons-cli-2.0.jar:/opt/zimbra/lib/dom4j-1.5.jar:/opt/zimbra/lib/log4j-1.2.8.jar:/opt/zimbra/lib/commons-httpclient-2.0.1.jar com.zimbra.cs.localconfig.Main -q -m shell mysql_directory mysql_socket zimbra_mysql_user zimbra_mysql_password