Twproject release 6.3 include the upgrade to Apache Tomcat 7, so before proceeding with the upgrade read this post carefully. Before proceeding do a complete upgrade.
In case you have installed Twproject with the graphic installer you can proceed as usual, download the new installer and launch it, it will upgrade the folder for you.
The installer will create a new service running on port 8080(for Tomcat 7) if you are running on a different one. Remove the old service (or disable it) and change the file server.xml( [twroot]/conf/server.xml) :
Locate the connector tag
<Connector port="8080" maxHttpHeaderSize="1048576" maxThreads="150" minSpareThreads="25" maxSpareThreads="75" enableLookups="false" redirectPort="8443" acceptCount="100" connectionTimeout="20000" disableUploadTimeout="true" URIEncoding="UTF-8"/>
and change the port number to your preferred one, then restart the service.
If you have HTTPS enabled you have to configure the new server.xml as the old one.
In case of a manual installation, that is already running on Apache Tomcat 7 you can proceed with the standard method: download the new webapp folder and upgrade it on your server.
If instead, you did a manual installation on Apache Tomcat 6 or lower you need to upgrade the webserver before upgrading the Twproject Webapp.
Here you find the Apache Tomcat guide for the upgrade: