I recall that some years ago Aeroflot Superjet 100 made an overweight landing and burst into flames. (SU1492) I read the reports and the aircraft was 1.6 tonnes overweight over 41 tonnes MLW. That would be 3.9 per cent overweight landing, and half of the people burnt to death because landing gear collapsed and punctured wing fuel tanks - leading to a large-scale fire.
Yes, I saw this mentioned up-thread, and it made my blood boil.
1) It was eight months ago, not years
2) The aircraft landed heavily, very heavily. There is a video showing it bouncing down the runway - not pretty at all.
In case English isn't your first language, I am saying the aircraft hit the runway hard, not because of the landing weight, but because of other factors such as possible windshear, or maybe the pilots were flying manually after years of relying on automation to smooth out their clumsy technique. Like the Delta pilots, they were also probably in a bit of a panic, which is not the best way to fly a plane.
The second bounce impacted the runway at 5.85g, and the third bounce at over 5g. That's equivalent to being 400% overweight!
In simple terms, SU1492 could have landed at minimum
landing weight, with the fuel tanks near empty, and the undercarriage might still have failed after such heavy impacts.
Obviously a badly controlled landing (e.g. after a microburst) stands a better chance of survival if the whole aircraft is lighter, but it is percentage points better. Being slightly overweight is not the main issue.
Where the full tanks mostly came into play with SU1492 was that the ensuing fire was much more widespread and lethal.
...this Delta aircraft seems to have been around 260 tonnes before dumping fuel, which is around 47 tonnes above MLW at 213 tonnes. (22 per cent overweight)
You can land a commercial aircraft well above max weight it is just going to need an inspection prior to flying again.
"In real conditions, with something going slightly wrong - one engine out, and landings conditions not that perfect - what are safety margin like for overweight landings - can something else afford to go wrong or is it like something else goes slightly wrong and somebody gets seriously injured?"
The phrase you are looking for is "what if the holes in the swiss cheese line up"?
You might as well contemplate what are the chances of winning the lottery, and then being hit by a bus before you can collect your prize.
Statisticians at insurance companies earn their corn calculating such multiple concurrent events.