How do airlines compute weight allowances for carry-on bags?

She said the 7 kg limit applies to the things we put in the bag, not the bag itself.

That's incorrect, the weight of the bag counts towards the 7kg limit. The Emirates webpage on baggage allowances (mirror) says nothing about ignoring the weight of the bag itself.

According to Skyscanner, the cost to check in oversized hand luggage (= carry-on bag) with Emirates is 158 AED (~= 43 USD) per kilo at the airport (but the price may depend heavily on the route), if you happen to get caught.

The cabin baggage tester (like this one below) shows what size and, if it has a weighing capability, what weight the bag has. If it is weighed separately, the weight of the container (bag/suitcase) is included in the baggage weight.

A 6 kg carry-on when empty is not unheard-of, but it is quite on the heavy side, and if they decide to check and enforce the weight limit there's no allowance left for any contents.

My experience has always been (on Emirates and other airlines) that they don't check the actual weight.

But, knowing people who often carry photographic equipment, their approach is to wear a photographers/fishing (or other) jacket or vest, which has many pockets and pouches that can hold lenses, camera accessories, etc. Your clothing is not subject to luggage limits. They simply remove the jacket/vest and put it in a tray for the security screening, and then wear it onto the plane.

Emirates has a 7 kg (15 pound) limit for carry-on luggage. ... But my carry-on bag, a 21-inch bag with a hard shell, weighs about 5-6 kg when it is empty. ... I can't see how they could expect me to fly 20+ hours (total, one-way) with only 1-2 kg of actual "stuff"...

I just want to point out that your line of thinking here is incorrect. You are framing this as Emirates' fault. However, Emirates does not decide the weight of your carry-on bag; you do. Your 5-6kg "bag" (more of an armored case), which consumes virtually all of your allotment, is your choice, and it is obviously a very, very bad choice. To call this Emirates' fault is absurd; your bag choice just doesn't work, and for some reason you can't see that.

I get where you might be accustomed to doing this on other airlines, but then, I would say fly those other airlines. Clearly Emirates plays by different rules, and you need to follow them to collect the cost savings that drew you to Emirates in the first place.

Obviously, the weight alone is a showstopper. Nope. Nope.

Certainly, at 21", there is no possibility of putting this under your seat, and it will have to go in an overhead bin. So claiming you need it for things needed during your 20+ hour flight doesn't make much sense either. You would not be able to access this bag without making a huge fuss: pulling it down out of the overhead (which might be quite far from your seat!!!) and jostling other people's bags as needed, taking it to your seat, opening it only partially because there's no room to open it fully, then rifling around in it to get the item of your interest, then taking it back to the bin and again rearranging everyone else's bags so your bag fits. What a fiasco. Maybe you're used to doing that whenever you fly, and don't realize how absurd it is, but try it.

The 7kg maximum weight greatly limits the potential volume of the items. You don't need, and can't use, anything near a 21" bag.

In fact, 7kg of stuff would easily fit under your seat. And now you're talking! This is a space that is yours, you control it, nobody else can damage a bag there, and you can access it almost anytime during the flight with very little fuss.

Further, you don't even need rollers for 7kg, so there's no reason for a heavy hardback, extendable handle, rollers, or any of that deadweight. All you need is a shoulder strap that might weigh 0.1 kg.

There's a parable of the person trying to push a river. They mean when someone gets up a full head of steam, hell-bound and determined, to do something at all costs that is in fact totally impracticable. In this case, you are "pushing a river" with your willfulness to use this very poor choice of luggage. As such, our job is to snap you out of that, and bring you back to practicality.

You need a new bag :)

I recommend a very light 0.5kg or less canvas bag with a shoulder strap. No wheels, no handle, no rigid structure of any kind. It needs to be a feather. And it needs to go under the seat. Its job isn't to protect anything, that's the job of you and the camera bag.

If the electronics going in this canvas bag need better protection than the item case (e.g. camera bag) provides, then upgrade the item case. Because armoring the camera bag or using an Otterbox for a phone is much lighter weight than armoring all your stuff for the sake of the camera.

As all other answers have pointed out, the limit is most definitely on the total of the case and its contents.

5-6 kg for a carry-on is just way too much. You should use another bag or case. Even with a hard shell, you can find cases that weigh under 2 kg for a carry-on, including wheels, handle and all, and some of them are very, very durable.

I had a similar issue with full-size suitcases before. Before you even put anything in them they already weighed half of the allowance, so I was always struggling to stay under them. I switched to a lightweight hardshell (with 4 wheels) a few years back, and it changed my life, I nearly never have to fear being over the limit.

So, cutting it down to the essentials, the bag weighs about 12 kg when full. According to my wife, who has flown with this airline before, this isn't a problem. She said the 7 kg limit applies to the things we put in the bag, not the bag itself.

No, as the other answers correctly observe your wife is not right. It's the weight of the bag in total that counts, not the content itself. However, it's a somewhat easy mistake to make, since many airports / airlines in fact do not enforce the various limits very rigorously:

• Most airlines / airports don't actually measure the size or weight of the carry-on bags, so there is a very good chance you may get away with a bag that's 12kg (I have certainly seen people carry stuff that looked a lot more heavy than 12kg). If they measure, they often care more about dimensions than weight, since in a plane the limiting factor often is space in the overhead compartments, not total weight of the airplane.
• Further, the "one carry-on per person" rule is, at least in my experience, hardly ever enforced. I have been travelling with a carry-on bag plus a separate laptop bag (which also stores most of my personal items), plus, in some cases, a duty-free bag, for years, without ever having been called out. My suspicion is that airlines in general don't care much about any items that are small enough that they can ask you to put them between your legs flight if the overhead compartments are filled. So I recommend taking your photography equipment out of your bag and carrying it on your body somehow.

But my carry-on bag, a 21-inch bag with a hard shell, weighs about 5-6 kg when it is empty.

Note that this is rather heavy for a carry-on. With 21 inches it also just barely fits Emirates' size restrictions. It's not that Emirates expects you to only carry 1kg of stuff in your carry-on, it's that they expect you to have a bag that weights 2 or 3kg empty, not 6. To be frank, this is not Emirates' fault.

What can happen if they enforce the limits?

(you didn't actually ask this, but it seems salient to the question)

Normally, when the airport or airline crew determines that your carry-on is too large, they will check the bag in for you directly at the gate. This may not be what you want if you have sensitive equipment in your bag, hence this is another point for having your camera equipment on your body rather than in your bag. You could in principle start re-packing when they ask you to check your bag, but I would be expecting some extremely displeased ground staff or flight attendants if you delay the boarding of a long-distance flight in this way.

An empty carry-on weighing 5-6 kilo is very unlikely. If it is correct, just replace it with something a bit more modern. I fly a lot in Asia and between Asia and Europe and I’ve mostly seen 7 kg limits for carry-ons. Whether it gets checked or not is a different matter, but your wife is definitely wrong about it being about the contents only.

As others have noted, 7kg is the limit all up.

IMPORTANTLY The following point is made in anough detail to hopefully dissuade you from "trying it on" with an overweight carry on bag -

On a number of occasions I have seen people systematically intercepted, in the security area where they cannot go back, to have their carryon bags weighed by people who are well aware that they are causing significant inconvenience and in some cases significant loss to passengers who are compelled to discard (lost irrevocably) items until GROSS weight is <= 7kg.
In this case, if you wanted to retain the camera you'd lose the bag.

It was not obvious why these people would choose to set up their operation in a location that ensures that the passengers whose baggage is deemed overweight have NO recourse but to discard and permanently lose property. This is WHOLLY unnecessary, highly & unnecessarily punitive and has few redeeming features as an approach - apart from ensuring future compliance at the cost of a deep dislike for airport security in general. In addition, where I have seen it done it seems (by my no doubt flawed perspectives) to have been done with glee and unnecessary harshness.*

I have seen this more than once. The passengers involved were headed for a range of flights so the action MAY have been airline independent. YMMV.

When I have noted such actions I watch the pattern of pouncing and time my transit to pass by while they are engaged with processing their latest unfortunate passenger. My carryon ALWAYS weighs no more than the apposite limit, but I do not wish to deal with such people more than I can help.

Related:

I have seen random bag checks of passengers as they enter the security area. "Randomly selected" passengers are taken aside to have their baggage contents rumbled through in detail. Again, there are only so many people employed on such tasks and one can time one's passing by to avoid them. Maybe not always, but I've managed so far. Again, this was done to passengers from numerous airlines so the policies of a given airline may not be a factor.

I had similar happen to me once only inbound to China at an Olympic city (Qingdao) during the Beijing Olympics. I was NOT randomly selected. My bag was last onto the carousel. I thought it was happenstance. it wasn't :-).
I had a full electronic workshop of tools and components in my luggage. I was taken to a backroom with 6+ security people who went through ALL my technical gear and asked me about it. It was "quite fun" as I knew I had a good reason for all I carried and they had a genuine concern due to the Olympics. But, still something to be avoided more than once, if possible.

*I accept security checks as a necessary part of international travel. Additional checks which cause substantial and unnecessary loss or gross inconvenience to some passengers, less so.