Short answer: No, you will not get such a discount.
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:
- Cost of paying the flight crew.
- Cost of paying the cabin crew.
- Cost of paying the ground crew (baggage handlers, maintenance, wing walkers, etc.)
- Cost of paying the check-in agents, gate agents, and other customer service personnel.
- Cost of paying all of the administrative staff back at corporate (marketing, executive staff, IT staff, logistics planners, weather forecasters, dispatchers, etc.)
- Amortization of that $246 million A330-300.
- Maintenance of said $246 million aircraft (parts, hangars, ferry flights, etc.)
- Airport fees (landing fees, gate fees, hangar rental, check-in desk rental, etc.)
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:
- A certain amount of floor space in the passenger cabin (namely, the amount your seat occupies,)
- A certain amount of carry-on baggage, and
- A certain amount of checked baggage.
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:
- The Maximum Takeoff Weight (MTOW) of the aircraft. For this, all weight on board does matter.
- The weight limit of the particular cargo deck itself. For this, only cargo weight matters.
- The weight limit that any one baggage handler is required to lift by himself. For this, only the weight of your one particular bag matters.
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.