Why are airlines so concerned with checked baggage weight?

Why is it that commercial airlines are so concerned with checked baggage weight, such that they charge extra just for the privilege of checking in a suitcase with a limited weight (e.g. 15kg), and then if you should go even a couple of kg over the limit, they charge quite a bit per kg?

My first guess is they see it as a way of making extra money, but is this the only reason?

The reason I'm so puzzled about it is that they don't seem the least bit bothered about the weight of carry-on luggage, not to mention the passenger's weight (e.g. I weigh about 70kg more than my daughter, yet our ticket prices are the same). And then the weight of the aircraft itself - e.g. an Airbus A320 weighs 42.6t, with a max take-off weight of 78t according to Wikipedia. So why are they so concerned about an extra 3-4 kg in the checked-in luggage?

3 Answers
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Airlines do care about your carry-on weight and even your weight. Many have carry-on weight limits, which low-cost carriers usually enforce, weighing the carry-on and tagging it as cabin luggage. Full-service airlines rarely bother.

One reason they don't measure your weight is that most people wouldn't feel comfortable getting weighed in front of strangers, then charged for that. Only Air Samoa currently weighs each passenger and tickets them by weight. In the West, weight is a contentious issue, so an assumed average is used for passengers. Such assumptions have crashed small planes, and in special circumstances like sports charters, actual weight is used. Finnair weighed volunteering passengers to get a better sample.

Weight costs money to carry, and not just in fuel burn. Luggage shares its volume with cargo, which airliners from the A320 up are designed to carry in the hold. Lately, cargo tends to get become more profitable than passenger service. Electronics and other high-value items cost more in depreciation and time value to ship by sea and land than by air, creating massive demand for air freight.

The A320 is 42.6 tons empty, but that's not the number that matters. The number that matters is its 78 tons MTOW, and how short of that it comes after adding pax, luggage and fuel to the 42-ton OEW. That spare weight is money in standby cargo.

Giving potential 175 passengers an extra 20 kg each (long-haul FSA vs average LCC allowance) could, if everyone used it all, add up to 3.5 tons total. Freight rates vary widely, but on a 3,000 mile flight that's worth $7k-$10k in freight revenue, or $40-$60/pax. Admittedly that's on the upper end of the range, but you can see there's money to be made. For an A320 that only costs ~$7k/hr to fly, it's a lot.

Less ethically, moving weight and volume from luggage to carry-on is profitable for a mixed passenger/cargo airline. Checked-in luggage has to be weighed in all cases, to ensure each piece is within safe limits for manual handling. This known weight then eats into the takeoff weight calculation, leaving less for cargo.

As airliners are designed to take off with one failed engine and carry reserve fuel for failures and diversions, this extra power works as weight safety margin when nothing fails. In practice weight margins rarely get pushed - most flights are volume-limited, with enough weight margin to take off at reduced power. Still, less luggage means more cargo means money.

Never mind the weight of the passenger and its flying consequences. For checked luggage, the main constraint is the maximum weight that has been negotiated with the bagage handlers' union. The passenger is assumed to be handling their carry-on luggage, and if they are stupid enough to injure themselves doing it nobody else particularly cares. But checked luggage is handled by employees, who often lug bags all day long. So keeping to a weight limit is important to preserve their health and safety.

You can draw your own conclusions about working conditions from the fact that domestic US limits are so much higher than international ones. And of course none of this prevents airlines from separately gouging the passengers with extra fees as much as possible.

If an airplane is too heavy when it tries to take off, it might not be able to take off safely (it might still lift off, but be unable to maintain flight in the event of an engine failure).

Additionally, the weights of the things that can render an airplane overweight (mainly passengers and their baggage) are not necessarily centered within the airplane's safe center-of-gravity (CG) range; thus, overloading a plane with passengers and baggage could potentially move the CG beyond its forward or aft limits, resulting in loss of control upon liftoff or shortly afterwards.[1]

The absolute upper limit on how heavy an airplane can be and still take off safely is known, conveniently enough, as its maximum takeoff weight (MTOW); this is the maximum weight at which an airplane is capable of lifting off and remaining airborne, even if it loses one engine at the worst possible moment during the takeoff. Note that the calculation of a particular airplane's MTOW assumes that it will be taking off from a long, dry, sea-level runway with a high local atmospheric pressure, engines at full power, a stiff headwind, and flaps and slats fully deployed; when taking off from a shorter runway, or from one covered in slush, or from an airport at high altitude, or with a low-pressure system over the airport, or with a tailwind, or with noise restrictions that require the use of less-than-maximum power when taking off, what matters is instead the maximum permissible takeoff weight, which is less than the MTOW (how much less depends on all of the above factors, along with any others that would make it harder to take off).

As a result, airlines try very hard to keep their planes from taking off overweight. There are eight major contributors to an airplane's weight:

Here's a diagram showing most of these contributors:

(Image by Mohsen Alshayef and NikNaks at Wikimedia Commons.)

Of these, the weight of the airplane itself is fixed and unchangeable from flight to flight (unless maintenance and/or repair work has been done on the plane in the interval between flights, which could slightly alter this weight). And the amount of fuel and oil carried is determined by the amount of same needed in order to get the airplane from its source to its destination, fly around in a holding pattern for an hour or so, and then fly to the diversion airport listed in the flight plan, plus a generous margin of safety to account for such things as headwinds, fuel leaks, engine failures, or all of the above simultaneously. This leaves six weights that can be minimised:

As you can see, most of the contributors to an airplane's weight either can't be lightened at all (airplane, petroleum byproducts, passenger chow), would incur significant cost penalties in lightening (passengers, freight), and/or wouldn't free up enough weight from being lightened (crew, passenger chow); this leaves baggage (both checked and carryon), and, since the average passenger has more checked baggage than carryon baggage, checked baggage represents a greater opportunity for weight reduction than carryon baggage does.

[1] As happened to, as previously stated in this comment by Michael Hampton, Air Midwest Flight 5481.

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