If your log tables are filling with entries, you should be able to clear the log tables in your database and that would reduce your site size. Have you tried clearing the entries from those tables yet?

Maybe check out Mitchel Sellers and Iowa Computer Gurus website. I believe they had previously created a scheduled job that would go in and clean these tables at whatever interval you select for the scheduled job to occur.

Also, for the logs to be getting filled there may be errors occurring. Any specific module or page that is throwing errors that could cause this or do you just have a very highly trafficked website? If it is a module or theme causing the increased number of log entries then getting those fixed could assist.

Just thinking out loud here...

Hope this helps..