As mentioned above you should start looking in to heap dumps. You can use JMeter to run scripts and get heap dumps at different intervals. This will help you analyse application memory consumption at different times.
Jprofile is also a great tool that can give you snapshots of memory upto the method level. Also run your weblogic with verbose option which provide memory statistics and you will be able to see the consumption of memory changing in logs as well.
How do you know there is a memory leak? may be your application is not provided enough space to process all the requests it is accepting.
I would confirm there is indeed a memory leak by connecting to applicaiton from jconsole and generating average and steady traffic for 6 hours.
Or you can skip this step and go to JProfiler / HeapDump analysis straight away, but would not help unless you already know what kind of request to your app is causing memory leak.