Do I need a re-entry permit for my non-immigrant O-A multiple entry visa if I leave Thailand and return after a few weeks?

If you are in the First Year of your O-A Visa then no Reentry Permit is needed (because it is a Multi-Entry Visa). If you are in the Second Year of Permission to Stay in Thailand you must buy a Reentry Permit

On a non O A you have one year of validity on the visa.. So within that year you will get stamped in for a year every time you leave and re-enter the country. You can exit and re-enter just before the date of expiry to get another full year of stay. But if you leave and re-enter the country after the original visa has expired, you will need to buy a re-entry permit as to not cancel the permitted to stay date you already have. If you are already on an extension of stay, from immigration inside Thailand, then you always need to buy a re-entry permit to not cancel your extension.

Do you have a visa issued outside of Thailand or an extension of stay issued in-country? Your post is a bit confusing.