If I weighed 120 kg I could check in 20 kg of luggage for free, getting 140 kg transported for my ticket price.
But if I weigh 70 kg, I'm 50 kg lighter and yet pay the same for the same luggage limit; and pay excess charges if my luggage is say, 25 kg and exceeds a 20 kg limit.
So what I pay for transporting 95 kg could cost more than the person transporting 140 kg.
Is there an airline that has a fairer policy and charges more appropriately based on actual mass transported?
Short answer: No, you will not get such a discount.
Longer answer:
For any significantly-sized airliner, the commodity they have to sell you is floor space in the cabin, not weight. If you're occupying one seat of the same size, you're costing the airline almost exactly the same as someone who weighs twice what you do.
Let's consider some numbers:
Assumed average weight of a passenger: 150 lb (68 kg).
Operating Empty Weight of an A330-300: 274,500 lb (124,500 kg).
Weight of the 293 passengers on a Delta A333: 150 x 293 = 43,950 lb (19,940 kg).
Example fuel load on an A333: 150,000 lb (68,000 kg). (It can carry up to 175,170 lb. (79,460 kg) of Jet-A)
Total before cargo for our fully-loaded A333: 468,450 lb (212,490 kg).
Now let's say we double everyone's weight. Adding another 43,950 lb (19,940 kg) adds another 9% to the gross takeoff weight for our A333 full of 300 lb (136 kg) passengers.
Also, one must consider that fuel is a major operating cost for airlines, but far from the only one. The other costs for operating your flight include:
All of these costs add up so much that fuel costs represented only 27% of costs for Delta in the most recent quarter and they were on the high end.
So, our A330-300 full of 300 lb (136 kg) passengers would only increase airline costs by around 9.38% x 0.27 = about 2.5%.
Conclusion: Your below-average weight is decreasing airline costs from those of flying an average 150 lb (68 kg) passenger by probably a fraction of a percent. This is certainly not worthwhile for the airline to create such a small discount, especially not considering the business they'd likely lose over people not wanting to be weighed and/or feeling discriminated against and/or feeling that their privacy is being violated.
In addition to the title question of whether you can get a discount for weighing less, baggage was also mentioned. The situation is a little different with baggage and actually varies depending on the type of baggage.
What you're paying for when you buy a ticket is:
The reasons for this are:
With carry-on baggage, you're again paying more for space than for weight. There's only so much volume available for carry-on baggage in the passenger cabin, so there are limits to how much any one person can bring so that, hopefully, everyone can get theirs in. No U.S. airline I've flown on has ever even bothered to weigh carry-on baggage. They only care that you have no more than the allowed two pieces (namely, one that will fit in the overhead bin and one that will fit under the seat in front of you.)
Some non-U.S. airlines I've flown on have weighed carry-on baggage, but only for safety purposes (i.e. to make sure it didn't exceed the weight capacity of the overhead bin.) In those cases, overweight bags didn't have an extra fee, but were rather banned outright, since it was a safety concern, not a cost concern.
With checked baggage, the situation is a little different. As densely-packed as passenger cabins may feel these days, the reality is that they're mostly filled with air. That's not necessarily the case with the cargo hold where checked baggage goes. It still has volume limits, but its weight limits also become significant, since the cargo is packed much more densely than the passenger cabin.
With cargo, in addition to the volume limits, there are multiple weight limits at play:
In practice, the last of those ends up being the reason for overweight bag fees. If your bag weighs more than an individual handler is required to lift by himself, they'll need multiple handlers and/or special equipment every single time they handle your bag, which can be quite a lot of times. It's for this reason that you'll be charged an extra fee for carrying one 55 lb. (25 kg) bag, but not for two 50 lb. (22.7 kg) bags.
Of course, as long as the bags are all under the maximum a handler is required to lift, more bags means more cost to the airline (it takes them 5 times as long to load five 10 lb. bags as one 50 lb. bag, for example.)
So, for checked baggage, you're usually limited both to a certain number of pieces and with a weight limit on each piece individually, rather than just a total baggage weight limit. How much you personally weigh is completely irrelevant to the airline's expenses for transporting your baggage. And, of course, again, this is in addition to the fact that the airline would lose revenue from passengers who didn't want to provide their weight, even if it otherwise would make sense for them to consider passenger weight in fares.
Samoa Air does, but the demographics make the reason for that obvious. http://www.telegraph.co.uk/travel/travelnews/10127347/Samoa-Air-introduces-XL-class-for-larger-passengers.html
Also an individual passenger's weight is not that important until we are on very small planes.
A big reason airlines want to keep baggage weight down isn't because the weight of the baggage (or passengers) directly increases fuel consumption (or other direct costs) but because baggage carriers have to move those bags. If everybody has bags that are unwieldy from weight or size then it will take a lot longer for the throwers to move the bags to/from the cargo bay. It doesn't do the baggage handlers any good that the passenger associated with a really heavy bag is slim.
Get a big coat, with lots of pockets.
No-one on a regular airline is going to give you a discount for being slim. You still occupy a whole seat, don't you? If you are so overweight that you need two seats, that's another story. They'll rightly charge you double. A while ago Ryanair charged triple for people who need two seats due to obesity or other reasons (such as having a leg in a cast.) I don't know if that's changed.
The price of excess baggage is just a huge moneyspinner. It doesn't really cost the airline $20 to fly an extra kilo, but they'll charge you for it if your bag is overweight.
Just get a coat, and stuff the pockets as full as you can. You can get 5kg in there if you have heavy stuff. And stick a book down the sleeve.
If you're carrying shoes and boots, wear the boots on the plane. You'll have to take them off at security, which is a hassle, but you'll save money.
Another trick is to put your stuff in a duty free bag. Generally the airports won't let the airlines charge extra for duty free, and no-one's going to check what's in there.
The answer given by reirab is a very good one. I'd like to add the aircraft operations perspective. For airlines, having passengers pay based on their weight is non-trivial to implement.
Before a flight, the airline must determine the total weight of the aircraft. This includes the weight of all people on board. The aircraft may be full of very skinny people, if the airline doesn't quantify how much lighter than are compared to average, then the airline can't optimize their operations accordingly (e.g. they can't reduce the amount of fuel on board or carry extra cargo).
If the aircraft has more than 10 seats, then the airline must either weigh each passenger individually with their hand luggage or use a forfeitary value. To give an example, during the winter on a plane with more than 30 seats, the weight of all passengers can be counted as
84 kgs x number of passengers
So for instance, if you weigh 45 kgs, the airline can't carry 39 kgs of extra cargo and they can't reduce the amount of fuel aboard. You not being overweight is not actually saving the airline any money.
If an airline wants to use the individual weights of passengers rather than the forfeitary value, then each passenger must be weighed individually before boarding the plane. This solution has been considered by a few low-cost airlines, but has always caused a public outcry. Furthermore, the average weight of the passengers+hand lugguage will likely be very close to the forfeitary weight.
In the case of Samoa Air that was mentionned in another answer, it is my understanding that they operate aircraft with less than 10 seats. Therefore, the forfeitary weight they must use is 104kgs per man and 86kgs per woman. In this case, using actual weight rather than forfeitary weight can make a difference. Furthermore, they can use passenger declarations rather than weigh each passenger, making it easier to implement.
They aren't charging you for your weight, they are charging you for the seat you are taking up. It doesn't matter if you weight 120kg, 70kg or 30kg, you are still going to take up one seat. So, except on rare occasion (like Somoa Air), they will never give you a discount for weighing less.
