I've never heard of any issues with size of WebLogic log files (as long as you have sufficient disk space for the log files). So maybe something else was going on. I would suggest you check the last entries in the log (before web server hang) to see what type of errors were being logged. Maybe that will provide some clues.
If the issue re-occurs, I suggest you get a thread dump. Below are a couple "My Oracle Support" knowledge documents that discuss how to get a thread dump and how to analyze a thread dump:
Doc# 615445.1: How to Create a Thread Dump with WebLogic Server 5.10, 6.1 and 8.1
Doc# 649428.1: Troubleshooting WebLogic Issues
Also, do you have anything installed in front of the web server? (eg load balancer or proxy?). If so, perhaps there was an issue with the proxy or load balancer and it wasn't forwarding requests to Web server.
WebLogic Server (WLS) Hangs With Deadlocked Socket Close() and Poll() Threads on AIX [ID 950347.1]
Also, there could be limits on the size of a file in AIX, but it is unlikely that the limit is lower than 1Gb--check the ulimit settings for the user that starts weblogic (use ulimit -Sa to see all limits, or ulimit -Sf for the filesize limit--note that the value is the number of 512-byte blocks).