Android - Can i delete old WhatsApp database backup without affecting the chat?

No deleting old backups would not delete all your chats but only the ones which you deleted before last backup was created and hence are not in latest backup. so you can keep the latest one without any fear of losing whats important to you.

Like it is said already, the chat is not touched by all these backups. You can delete them without any harm.

The thing is, it won't help you nothing to delete these. WhatsApp will rebuild them day after day till they all are back. You cannot change this backup behaviour of WhatsApp. The only thing to get the backups smaller is to delete your chats and delete the WhatsApp data. Then not restore the existing backup when WhatsApp started first time after data-deletion. But who wants this?

EDIT 2017-04-05: I wrote a little Task in Tasker (need root for it!) which deletes all these old backups each night. This saves me some 100 MB of space :) I use the Action "Run Shell" with a "rm" command with wildcard. Works :)