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I was told that if the aircraft's weight exceeds the maximum landing weight, it could cause a structural damage during landing, but why?

My understanding is that with a heavier aircraft, I need fly with a faster approach speed; but if the runway is long enough, I could land with more lateral energy with minimized vertical energy without causing any structure damage, is that right?

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At the instant of touchdown, any vertical kinetic energy the plane possesses must be absorbed by the landing gear, which thereafter must bear the entire weight of the plane. That kinetic energy depends on the sink rate and the plane's weight.

The sink rate ideally will be zero at wheels down in a perfect world, but the gear is designed to accomodate a certain range of sink rates and plane weights via compression of its spring struts and shocks. If either the sink rate or the plane's weight causes the maximum compression range to be exceeded, the suspension will run out of travel and bottom out hard and the resulting shock can damage the attachment points of the gear to the fuselage or the gear itself- or even cause the gear to collapse.

The maximum gross weight at takeoff (full tanks, maximum payload) is set by engine power and wing lift when configured for takeoff and the expectation is that by the time the plane has reached its destination it will have burned off enough fuel to be under the allowable gross weight at landing (which is set by the design of the landing gear as explained above). This means that the plane's designers can minimize the weight of the landing gear by not having to strengthen it enough to routinely accomodate a landing at maximum gross weight at takeoff.

And that, in turn, means that if a fully-loaded plane has to make a quick return to the line for any reason, it must dump fuel first.

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    $\begingroup$ ...and that for even quicker return the pilot can decide to overstress the landing gear if breaking the aircraft is not important in the current emergency. $\endgroup$
    – Manu H
    Commented Jan 7, 2020 at 7:46
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    $\begingroup$ Well, braking power also can limit the max. landing weight, and then it depends on the conditions (rwy length, winds, whether, altitude, missing thrust reversers, ...). $\endgroup$
    – yo'
    Commented Jan 7, 2020 at 13:54
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    $\begingroup$ One other thing to take in mind, is that brakes convert the kinetic energy of the plane to heat after touchdown. And you don't want your brakes to overheat $\endgroup$
    – Ferrybig
    Commented Jan 7, 2020 at 20:23
  • $\begingroup$ But if you report you are coming in ‘hot’ I’m sure they will have something to ‘cool’ you down waiting. $\endgroup$
    – vasin1987
    Commented Jan 8, 2020 at 19:33
  • $\begingroup$ @vasin1987 unless you insist it's “not an important fire”... $\endgroup$
    – leftaroundabout
    Commented Jan 8, 2020 at 19:59
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Maximum landing weight (MLW) limit exists primarily to cater for approach climb performance requirements (i.e. go-around requirement). As per 14CFR 25.1001: if the aircraft does not have a fuel dumping system, it must meet the all-engine-operating and one-engine-inoperative climb in the approach climb configuration at maximum takeoff weight. Otherwise, credit can be taken for maximum landing weight. So the design decision of whether incorporating a fuel jettisoning system or not comes down to this.

Landing gears are designed to land above MLW and even at maximum takeoff weight, with or without fuel dumping capability. 14CFR 25.473 requires that landing gear and supporting structures withstand a landing load at maximum takeoff weight at a contact speed of 6 ft/s. This is definitely reduced from the 10 ft/s design load for maximum landing weight, but is still larger than the typical landing speed of 2-4 ft/s. However, maintenance inspection would be required if landing above MLW occurs.

The need for fuel dumping has been thoroughly discussed in this question.

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    $\begingroup$ Would I be correct in my understanding that Maximum Landing Weight isn't the maximum weight at which the plane can land with minimal likelihood of harm to passengers and crew, but rather the weight with which a plane can be expected to land routinely without requiring extensive inspection for damage? If so, it might be good to mention that. On a long runway, a skilled pilot who minimizes landing impact may prevent the plane from being damaged, but operational procedures would require inspection even though that inspection might reveal that everything was in fact undamaged. $\endgroup$
    – supercat
    Commented Jan 7, 2020 at 15:48
  • $\begingroup$ @supercat yep, aircraft are performing overweight landing in exceptional scenarios, e.g. when something seriously bad happens after takeoff. $\endgroup$
    – yo'
    Commented Jan 7, 2020 at 16:21
  • $\begingroup$ @yo': Is there any factor beyond the possibility of damage requiring repair before an airplane could be reused that would limit an aircraft's landing weight to a value below the takeoff weight? A plane's takeoff weight needs to be such that a plane can safely get airborne even if an engine fails just after an aborted takeoff becomes impossible. Or is your point that the maximum takeoff weight on one runway might be less than the maximum landing weight at another? $\endgroup$
    – supercat
    Commented Jan 7, 2020 at 17:02
  • $\begingroup$ @supercat medical emergency, passenger posing safety threats, etc. for instance. $\endgroup$
    – yo'
    Commented Jan 7, 2020 at 17:30
  • $\begingroup$ @supercat It depends on each airline and each airframe. At my airline, if the landing is going to be overweight, the pilots note the vertical speed reading at touchdown. Maintenance can look up on a chart whether or not an inspection will even be required. So, depending on how soft the landing is, an overweight landing may have no repercussions at all. $\endgroup$
    – nexus_2006
    Commented Jan 8, 2020 at 2:34

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