We use 700x23 tires on the steel Kuwahara tandem, but crew weight is ~320 lbs and we never carry bags of any kind (a bike is not a pack animal!).
You can buy 700x20-23 tubes for CDN$2.50 or long-stem tubes (60mm) for CDN$2.75 from Mountain Equipment Co-op in Canada (mec.ca).
All the previous advice about checking for tire defects is excellent. One more thing I would add is to check the sidewalls. Some - especially Continentals - tend to crack from age. Contis are notorious for sidewall blowouts Sometimes the brake pads will move upward as the pads wear (this is particularly noticeable on the arm attached to the offset pivot on dual pivot sidepulls). If the pad is set too close to the top of the rim, it will sometimes contact the sidewall and wear a hole in it. Don't laugh - it's happened to me.
- L.