I am going to suggest JIRA. I think it is pretty lightweight. You can either run it with the built-in database or let it talk to MySQL or PostgreSQL. It runs without the use of an app server. Just unzip and run. http://atlassian.com/starter/
no offense, but JIRA is not in the slightest lightweight. JIRA is extremely abstracted out to be whatever you want it to be. It's good for project management and for different projects that require different work flows, but you definitely need to spend time in setting it up to fit your needs.