737 FCOM vs FCTM
 

Boeing clearly mentions in the FCTM that is advisory in nature.
FCOM has chapte called limitations with a Max Landing weight

Limitations should not be busted why does the FCTM write about an above weight landing then

*Except in an emergency

why does the FCTM write about an above weight landing then

I'd always been told that B737 can land at MTOW minus the fuel used during departure. There is no fuel dump and I suspect they wanted to avoid any committee discussions in the flight deck during an emergency.
As I-Crunk says, any a/c can land at any weight in an emergency. Sometimes it's better to be on the ground sooner rather than later.

I believe MLW is based on using 9 fps as the touchdown sink rate and the gear is tested to that plus proof margin. The plane and, obviously the gear, must be able to land at MGTOW at 6 fps or have a dump system capable of dumping fuel down to a weight compatible with the gear's strength.