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I'm writing a story about the aftermath and consequences of a runic magic system being mysteriously introduced to the human race by an unknown entity. Every week a new rune is given to everyone on Earth over the age of 13, and everyone can keep any six of their choosing before having to give one up to make room for the next week's rune. Each rune represents a supernatural power the bearer is capable of using.

Initially society manages to adapt and cope with this radical change in the status quo, but by the end of year one, various factors, both from the rune system and from malicious third parties, combine to cause total societal collapse, resulting in a very long period of time where civilization is struggling to re-assert itself, and the superpowered survivors of the initial collapse and dieoff fight to survive in the ruins of the modern world.

This brings results in a certain issue I need to address. You see, during that first year when things seem like they're going to be okay, several one-week-only runes grant humanity the opportunity to take part in transhumanism. Occasionally a new fantasy race is introduced to the world, and everyone on earth will be given a totally genetically randomized body as a member of that fantasy race that they can switch between freely for that first week, and keep forever (in exchange for giving up their old body permanently) if they so choose by staying in that body when the rune disappears.

One of these races is a fairy-like creature called a lightwing. They're one foot tall, can fly, and while they're significantly weaker and more fragile than humans, it's not nearly to the degree that their size would suggest. You see, I want lightwings to be strong and tough enough that while they are weaker and more fragile than humans, their strengths and weaknesses with the other races balance out, and a fight between a lightwing and a human of equal skill and equipment would be a fair fight.

But here's the issue I'm having: If an individual lightwing is a match for any other creature, then when the apocalypse hits and resources become scarce, the fact that lightwings are tiny (and thus require way less food, water and space to survive) would give them an insane advantage over the other survivors during the initial decades after society collapses. People would be fighting over scarce resources that would go a lot further for lightwings than for anyone else. I can't see any reason why they wouldn't utterly dominate the post-apocalyptic environment.

The supplies that would keep a small band of five human survivors alive would be enough to feed a veritable swarm of lightwings that those five survivors couldn't possibly hope to compete against. And then when people start re-establishing communities and growing crops, the lightwing population would explode (relatively speaking) from the small minority they were before the apocalypse to much larger populations than any post-apocalyptic human community would be able to feed. When it reached the point of open warfare between these communities, the lightwings communities would rip the competition to shreds through sheer force of numbers.

Now, I obviously don't want this, but I still don't want to make individual lightwings inferior to individual humans to balance out their superior numbers, because that would somewhat dehumanize them and make them way less interesting as individual characters, especially since I want the story to revolve around smaller groups rather than large-scale warfare, at least at first. My initial planned solution to this was to make lightwings require just as much food as any other humanoid despite their tiny size, but the problem with this is that the concept of a tiny humanoid consuming, digesting, and excreting several times its own body weight in food per day sounds like it's going to need some very careful magical handwaving to not seem utterly bizarre (and gross). I'm prepared to try and handle that if I have to, but it occurred to me that I might not have to. There might be some other option I have to make the lightwing "zerg rush" strategy less viable.

What else, besides not having enough supplies to feed them, would keep my small fairy creatures from assembling in larger numbers than humans with the same resources and attacking in swarms?

Flying creatures have a much higher metabolism for their size, especially non-gliding kinds like fairies. If you assume they have a metabolism similar to a hummingbird, then a 10 pound fairy will need just as much food as a full grown man; so, scarcity would be just as meaningful if not more so to them because not only do they need just as much food, but they will need to stop to eat more often because of their smaller stomachs and lesser body fat.

[edit] Aside from this fact, (since you asked for an answer that does not involve eating a lot for their size), what constitutes as a fair fight may be relative. Their speed and agility may give them the opportunity to out maneuver a giant warhammer for a quick slash to the neck, but their advantages may have well-known counters such as using nets, flails, water hoses, specialized armor, or other weapons & techniques that make it an uneven fight.

Basically, other races can adapt their methods to kill lightwings much more easily than the inverse; so, while they may do well in the opening days of a conflict, an enemy that is prepared to fight them will typically win, even if outnumbered.

They reproduce like cicadas.

Some small creatures take their time about reproducing. Some cicadas take 17 years to reach sexual maturity. That's more time than larger creatures such as dogs and cats.

Your fairies may reach sexual maturity only after they are 40 or 50 years old.

And then, like cicadas and so many other insects, they mate, lay eggs and die, all within just a few days.

That would make the loss of fairy life more dangerous to them as a species than the loss of a human life is to us. They will want to play cool with other races.

1. 
   Transhumanism runes are no longer available.
   
   If you and your family were hungry, and had the opportunity to change yourself such that you all would not be so hungry, probably you would do it. You are right that after the Fall lots of people would want to be Lightwings. But after the Fall (or at some point before) the Transhuman runes are no longer available. The Lightwings that already exist will not increase in number - there is no way to do it. Except possibly by breeding...

2. Lightwings have no inherent affiliation with other Lightwings.

If I am Latvian in the US, and somehow Latvians have a survival edge after the Fall, I will find other Latvians. For one, I go to church with a bunch of them. I have been to their houses. For two they speak and read Latvian. I can put up signs. Also there is a restaurant we all used to go to and so I would recognize them if I saw them. They think like me, we have a shared background, we can talk and we get along. We can definitely team up.

Your Lightwings are raised human. Their families are human and their background is their human background. The only thing I as a Lightwing have in common with other Lightwings is that at the time Lightwing bodies were on offer, I thought they looked cool and I thought I would try it out. I chose Lightwings because I have always been hot for Tinkerbell but maybe it turns out that a vast majority of people who chose to be Lightwings chose that because they were old and aching and very heavy and were tired of it. These old folks qua Lightwings like to complain and argue, and voice their suspicions about what kind of people the other Lightwings were before they were Lightwings. They are not much for the teaming up.

My buddies, on the other hand, are a bunch of other things besides Lightwings. In once sense that is a shame because there is no Tinkerbell equivalent, but otherwise it works well. It is easier hanging with them because they are not fussy old jerks and actually our strengths complement each other.

Because lightwings are solitary creatures. To the point of being unable to exist with other lightwings unless it's mating season.

They explode.

You move one lightwing to another one and closer they get they start to magically vibrate and when they touch they resonate with each other channelling their inner magic on the same oscilloscopy level of recipient and it make them explode.

Also ancient curse. Modern curse. that one rune that make them die. and that spell that make more than three lightwings on square meter turn into hotdogs.

You say they require less resources because they are tiny yet still are equal in a fight with a human. But why wouldnt you just say "they might be tiny but still use similar amount of food and water as humans"? Give them an ability for eating a lot in a short amount of time to shut people up about "tiny mouths=needs to eat most of the day" and you are done.

They eat things that humans do not, and that is as scarce as human food. You could make them reliant on some shared resource but have others be completely separate if you want to give them a reason to fight (they both drink water, but eat totally incompatible foods, for example).

This doesn't solve the living space issues - lightwings could fit in smaller spaces, but fighting over their scarce food means they isolate themselves into smaller groups. They may also need some special environment to be comfortable and happy. Humans like to be out of the weather and somewhere around 70 degrees. Maybe lightwings need very high humidity, or they can't handle extreme temperatures. Those examples might limit their range too much for your story, but some other acceptable requirement could limit their ability to congregate in large numbers but still allow them to live in various locations/environments.

If your fairies retain their intelligence then there aren't many options actually

Arrogance

Simple enough. Because of how easy it is for them to survive and flourish(as compared to non-fairies), they begin to believe the world belongs to them, all the more so when you consider their numbers. In other words, they develop a sense of manifest destiny. They don't go around in large swarms mainly because they see no need/can't be bothered to organize themselves sufficiently. Hostile encounters between fairies and non-fairies tend to be in small groups or even one on one because of a twisted sense of honour, which is probably just a veneer for sadism.

They're fascinated by bright lights, hence the name.

If your humans can survive the night, they'll find the entire Lightwing army staring stupidly at the sun, which is when most predators hunt for them.