Autcache + Varnish modules installed but cache tables growing
Varnish should not ideally affect your cache tables, not sure about auth_cache. You should try the reverse approach to figure out what is wrong, check which of your cache tables is growing abnormally and then do bit of digging around to find what module/s is responsible for stashing cache data in those tables.

There is a well-known issue with cache_form table in D7, it can grow abnormally for some live sites. Check this issue, Cache Form table size is enormous.

If you find your cache_form also huge you can use one these modules to help you to periodically clear it, https://www.drupal.org/project/optimizedb or https://www.drupal.org/project/safe_cache_form_clear.

Hope this helps.