I am somewhat concerned by how "serious" an overweight landing is considered above...
As far as I know,
any 2 engine aircraft will require effectively "Land ASAP", and at nearest suitable airfiield, after (even partial) loss of 1 engine - over MLW or not. Maybe there are exceptions... but for 757/767, A319/320/321 in my company this is the case. Some 767s (not all) can dump fuel, but only from Centre Tank, and there was no
requirement to get to MLW before landing, or even dump to max extent possible. In a 3+ Engine aircraft, I can see MLW being adhered to for a simple (single) EO.
NB sometimes the MLW is commercial - our MLW limit has changed for the A319 a few times recently. It is strange to need to do the "overweight landing checklist" (and engineer's checks) one day, but don't need to do the next day same weight / same aircraft
My main concern with overweight lanidng is the stopping / GA performance. The RoD / Inspection requirements are engineers' problems, not mine