This looks contra-intuitive: if a plane can take off and fly horizontally, what prevents it from descending and touching down to the runway with the required small vertical speed?
Because when taking off you go from 0 vertical speed to a positive rate of climb all by way of the wings (the force on the gear will decrease over time to 0 when airborne). But while landing you will go from negative rate of climb to 0 vertical speed. Most of that will be absorbed by the gear (the force on the gear will spike and then settle to only the weight of the aircraft). After touching down there is also the braking force exerted on the gear which is proportional to the mass of the aircraft.
It is that spike+braking force that the engineers are worried about when calculating max landing weight.
The two weights are not directly related: in theory max take-off COULD be less than max landing, but that would show an issue with the design.
Take-off is determined by available field length in effect, and thus the engine thrust needed to get the plane airborne (before you run out of field). And in fact, you need a long enough field so that at V1 you can stop and and not fall off the end.
So the designer has to have enough thrust to goose it into the air fast enough, with enough fuel to fly to where they need to get to. More engines is more mass, more expense, and more fuel to run them.
Landing is not determined by engine thrust, in fact engine size works against you a bit because bigger engines are heavier. Landing relies only on drag and brakes. In fact you CAN land with max take-off weight, but that's an extreme, and you might burn your brakes/blow tires. Max landing weight also has to take into account bad weather, which increases required runway length. Also has to take into account possibility you might not have full use of flaps for drag, so need combination of longer runway, and enough braking capacity.
Commercial jets are all about economics and the trade-offs made in the design. You don't NEED to have max landing weight the same as max take-off, except in case of an emergency right after takeoff.
If you download PIANO (the free/trial version) you can select various weights for take-off and landing. See what it does to the landing field lengths.
Remember also that there is an existing set of airports that the designers want their planes to be able to take-off from, and land at. Also that the routes they want to fly have certain distances, needing enough fuel to get there.
As you increase take off weight, you need more lift, and more thrust. And you have to do it in the available runway length. When you land, you can take advantage of that lift (since you got it from a bigger effective wing area) but you also need brakes. Brakes are heavy and cost money to build as well as maintain.
Take off weight will vary from low (just enough to get to a nearby airport) to the max: enough to get to the farthest one. Landing weight SHOULD ideally be the same: just the empty plane weight and the reserve. Anything more and something has gone wrong. So the designer aims for that, and builds enough safety into the system to allow a landing with max takeoff, but with the possibility of tires blowing, or at least having to wait until brakes cool.
I read an account of commercial planes flying into Kabul fully loaded with fuel for re-supply, and they had problems with hot brakes, blown tires etc. Commercial planes are not designed for that. True military tankers/freighters have more effective reverse thrust, and need to use it to land on short runways. And there is no concern for passenger safety for hard deceleration, nor for noise.
The main reason commercial jets don't use reverse thrust more is because of noise (and emission) regulations. Otherwise you could land as heavy as you wanted: reverse thrust can give you up to 20%-30% of max thrust, and is effective at high speeds.
And if you look at engine thrust, there is a huge difference between take-off max thrust and cruising. Once you are airborne, you don't need a very big engine. But you have to carry around all the extra bulk just to get into the air.
On short flights, one of the big issues is the time to cool the brakes. If you have a quick turn-around and not much time between your next landing then your brakes don't have much time to cool. In that case the max plane weights are not really the issue: you are not carrying much fuel.
Note: Airbus has data on how much reverse thrust each plane has. It is a function of N1 (fan speed) and air speed. See: Airbus Takeoff Safety
Ratchet freak's answer is entirely correct, but I would like to add to it. A plane could have a max landing weight that is equal or greater to the max take off weight. There is no technical limitation to it: the landing gear can simply be made to be sturdier.
However, sturdier landing gear is heavy and expensive. A plane will (usually) be lighter when it lands than when it takes off, because it burned fuel, so the additional sturdiness will seldom (if ever) be used. Therefore, manufacturers decide to make planes that have a safe take off weight that exceeds the safe landing weight.