What are different types of weights of an aircraft?
The different terms represent different weights or masses1. For each flight, the weights are taken into account for several reasons.
A brief description about these is below:
Manufacturer's empty weight (MEW)
Also called Manufacturer's Weight Empty (MWE) or Licensed Empty Weight
It is the weight of the aircraft "as built" and includes the weight of the structure, power plant, furnishings, installations, systems and other equipment that are considered an integral part of an aircraft.
This excludes any baggage, passengers, or usable fuel2.
Zero-fuel weight (ZFW)
This is the total weight of the airplane and all its contents (including unusable fuel), but excluding the total weight of the usable fuel on board.
As a flight progresses and fuel is consumed, the total weight of the airplane reduces, but the ZFW remains constant.
Maximum zero fuel weight (MZFW) is the maximum weight allowed before usable fuel and other specified usable agents (engine injection fluid, and other consumable propulsion agents) are loaded.
Operating empty weight (OEW) (Roughly equivalent to basic empty weight on light aircraft)
It is the basic weight of an aircraft including the crew, all fluids necessary for operation such as engine oil, engine coolant, water, unusable fuel and all operator items and equipment required for flight but excluding usable fuel and the payload.
It is the carrying capacity of an aircraft. It includes cargo, people, extra fuel. In the case of a commercial airliner, it may refer only to revenue-generating cargo or paying passengers.
Maximum takeoff weight (MTOW)
This is the maximum weight at which the pilot of the aircraft is allowed to attempt to take off3.
Regulated takeoff weight (RTOW)
Depending on different factors (e.g. flap setting, altitude, air temperature, length of runway), RTOW or maximum permissible takeoff weight varies for each takeoff. It can never be higher than MTOW. More information is on this answer.
Maximum landing weight (MLW)
This maximum weight at which an aircraft is permitted to land3.
The following image depicts takeoff weight components.
Maximum ramp weight (MRW)
also called maximum taxi weight (MTW)
It is the maximum weight authorized for maneuvering (taxiing or towing) an aircraft on the ground.
It is the total aircraft weight at any moment during the flight or ground operation. This decreases during flight due to fuel and oil consumption.
1: As mentioned (below in comments by SentryRaven), several recent references use the term mass instead of weight. Having a Physics background, I tend to agree and know the difference between weight and mass. I did not use mass as most of the references I included referred mass as weight. However, using correct terminology, all the weights mean mass. Thanks SentryRaven for pointing it out.
2: What is the different between usable fuel and unusable fuel?
Usable fuel is the fuel on board an aircraft that can actually be used by its engines. The small amount of fuel that cannot be drained from the tanks is the unusable fuel. For calculation of range, usable fuel is used. For weight and balance total fuel (usable + unusable) is used.
3: This restriction is due to structural, design or operational limitations.
AFAIK, they are no longer called weights but masses. The PPL training and examination material no longer uses MTOW but only MTOM: maximum take-off mass. The skybrary also refers to MTOM. Maybe leave a little remark in your otherwise very nice answer?
Also related (and alluded to above) are the two most common "load" figures: *Useful Load* (the maximum gross takeoff or operating weight minus the operating empty weight), and *Payload* (what the aircraft can carry in cargo/passengers/personnel when loaded with the fuel required to make the planned trip).
@SentryRaven Since the U.S. is still (foolishly in my opinion) not using the metric system as our standard, I doubt that we will anytime soon use M instead of W since pounds are a unit of force, not mass. Also, I think the SKYbrary entry could be better written. As it is now, it would likely be interpreted as saying the aircraft's mass in pounds does not vary by altitude when, in fact, it does ever so slightly. The change, of course, is insignificant for aircraft weight purposes.
I believe MLW should refer to footnote #3, so I changed that. Please revert if I'm incorrect
@Terry, As far as I can tell, "pound" is a unit of _mass_ (defined as 1 lb = 0.45359237 kg) and there is a "force pound", abbreviated lbf, that is a unit of force defined as 1 lbf = 1 lb × _g_ (_g_ is gravity of Earth), allowing people to be sloppy with their dimensions.
@JanHudec We may be looking at a generational thing. As I remember both my high school and college physics (1950s and 1960s), we were taught that in the English (Imperial?) system that the unit of mass was the "slug", the unit of force the "pound". The equivalent metric units were the Kilogram and the Newton. There was no mention of a "force pound."
@Terry, I think it's more a domain thing. "Engineering" system has pound for both mass and weight and live with _g_ coming up in Newton's second law, "Gravitational" system uses pound for force and slug = lbf·s²/ft for mass and "Absolute" system uses pound for mass and poundal (pdl) = lb·ft/s² for force. The first is most common, but impractical for physics, which is why the other two are used there.
@Terry, also note that the metric system actually has similar set of variations with units like kilopond = kg·_g_ and even hyl) = kilopond·s²/m, but these systems have fallen into disuse and SI became almost universal except for few uses of CGS, which is just scaled by powers of 10, and various natural units in particle physics and cosmology. While in imperial both mass-pound and slug are widely used.