I frequently do large grocery trips with my bike and the rear tire always looks smushed even at 80 psi (26×1.95). I was thinking of over inflating another 5-10 psi but not sure if this is going go lead to other problems.
I don’t think it’s a good idea to ever inflate your tire above the pressure that is listed on the outside of the tire. Maybe your tire is supposed to have more pressure than 80 PSI?
Have you checked the outside of the tire to get the recommended PSI range (see image linked here)? Use that as your guide to how much pressure to put in the tires.
If you’ve inflated it to that pressure and the tire still looks off, take it into a local bike shop and have them take a look at it.
Generally, if bike+rider+groceries > 250 lbs, you may to see some deformation of the tires at recommended inflation levels. Don’t overinflate, that just makes the tires/tubes more stressed out under heavy loads. Deformation is OK, just be careful of where you’re riding when hauling a heavy load. Hitting a hole or something will be more likely to give you a flat and bust up your rim.
You can get special tyres designed for tandems that can handle more pressure / load.
