What happens if an aircraft tries to land at MTOW (if greater than MLW)?
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.