Not easy
In a classic ( if that is what the a/c in question was) you have a real chance of heating up the brakes enough to blow the tires and cause brake fires when you land overweight. The higher you are over MLW the more likely you will loose the fuse plugs and have a brake fire or two.
Landing overweight is a serious event, not to be taken lightly. Yes the a/c (at least the Boeing) only needs an inspection if nothing catches fire but if the tires go it is a big problem.
Our co. had a 400 land overweight not too long ago and some plugs let go and there were a couple of brake fires.
All of which as described above would make de-planing a medical emergency very problematic.
Sounds like the crew did the best they could. Juggling a human life, the possible outcomes of overweight landing, the ATC dumping procedures and expectations was most likely a very stressful flight. Well done to the crew, hope the pax is alright.
FG