We can land both the 757 and 767 at max weight in certain circumstances. The 767 has a max take off of 181400Kg and a max landing weight of 136000Kg. If you dump all of the centre tank fuel (which is the only tank you can dump) you can still be overweight.
The 757 has a max take off weight of 99700Kg (artificially limited, it can be as much as 124000Kg) and a max landing of 90000Kg with no dump capability (this can also vary).
In overweight cases, you have to be of the opinion that a greater emergency will exist if you hang around.
Anything over the max landing weight is considered an overweight landing - more of a problem obviously with a 767 at max weight. It might not necessarily mean anything dramatic, but it could mean a heavier landing, greater risk of an overrun or brake fire.
A overweight landing check is required if you land over max landing weight - although no problems may have occurred.