Most (all?) modern airliners are, in fact, certified to land at any weight up to MTOW if necessary, but if they do land at more than MLW then a special "Overweight/Heavy Landing Inspection" must be performed before the aircraft can be used again.
As this Boeing document states:
Overweight landings are safe because of the conservatism required in the design of transport category airplanes by FAR Part 25.
FAR criteria require that landing gear design be based on:
A sink rate of 10 feet per second at the maximum design landing weight; and
A sink rate of 6 feet per second at the maximum design takeoff weight.
Typical sink rates at touchdown are on the order of 2 to 3 feet per second, and even a “hard” landing rarely exceeds 6 feet per second. Additionally, the landing loads are based on the worst possible landing attitudes resulting in high loading on individual gear. The 747-400 provides an excellent example. The 747-400 body gear, which are the most aft main gear, are designed to a 12-degree nose-up body attitude condition. In essence, the body gear can absorb the entire landing load. The wing gear criteria are similarly stringent: 8 degrees roll at 0 degrees pitch. Other models are also capable of landing at maximum design takeoff weight, even in unfavorable attitudes at sink rates up to 6 feet per second. This is amply demonstrated during certification testing, when many landings are performed within 1 percent of maximum design takeoff weight.