I did an overweight landing back a few years ago on an A320 due to medical emergency. (Passenger heart attack-Doctor said hurry and get on ground.) After the landing and talking to maintenance, they said the big thing is how hard was the landing? If it is over a certain G limit or greater than so many feet per second down then there is a long inspection to do on the aircraft. If you are within the limits it is a visual inspection only.
We did a good landing and had only the visual....I never knew what happened to the pax. I can't remember how much over weight we were but it was at least a few tons.