The user contacted me via Discord and I helped them resolve the issue, leaving the fix here:
The Classic Pack uses 'tabbychat' a litemod that enhances the default chat system. One of the default options includes chat history, which saves per-server/world so that players can quickly check what their friends said in private DMs. In this particular case, the user did indeed spam their chat with.. a lot of messages via the MineTweaker verbose.
The fix is to go into the root liteconfig/common/TabbyChat2/ folder and delete the singleplayer or multiplayer world.
Also worth highlighting that @Kuramai should avoid outputting to the client with MineTweaker and instead use the commands that output to the CraftTweaker log. Using a program such as SnakeTail really helps with this as it automatically reloads when it gets new information.