Send the final resume if the referrer has not submitted the referral yet.

The person referring you should ideally have the same current information that recruiting will see, especially if the system asks them to attach or review your resume.

A quick note saying 'I made a few final edits, attaching the latest version for reference' is enough.

Do not keep sending repeated minor revisions. Once the final version is ready, send it once and let them proceed. If useful, this guide on consulting referrals gives more detail.