Hi,
For some aircraft type like the A380, especially for long sectors, we can't jettison to max landing weight. This is due to the fact that the fuel in the feed tanks cannot be jettison.
For what I know, 380 is certified to land at Max Takeoff weight !! Thus, even for non-time critical fault we have to land overweight.
But of course, if there's a flight controls / landing gear problem, we might try to hold and burn the fuel just to go below our max landing weight.
Just my 2 cents worth,
Cheers