Txn Log backups - does it backup empty space?
Log backups only backup actual data and do not backup empty space.

It sounds like there are still processes running overnight.  Got any index rebuilds or any maintenance tasks (aside from DB backups) that may be running overnight?  Just because you think the server should be quiet, doesn't always mean that it is.  There could be overnight batch jobs, miscellaneous tasks, all sorts of stuff.