What database table can be emptied in order to make database lighter? Are log files in drupal take a lot of space? I want to create a dump file but it's over 1000mb. What tables can be harmlessly emptied from the database directly or through drupal interface?
Usually all tables with cache_ prefix are safe to be emptied.

The log table records can take a lot of space, depending on your settings on how many log messages you want to save. You can configure this at admin/config/development/logging.

How many nodes/users do you have on the website? Do you have enabled the core search module? What other modules do you have?

If your website has tens of thousands of nodes and users, 1GB is a normal size of the database dump.