The strength of a claim will depend greatly on need. In case of limited resources, the one with the greatest need has the strongest claim. In food terms, for example, if there is one bowl of rice left and everyone's satiated while one person is about to starve, their claim on the rice bowl is the strongest, so they are awarded the rice bowl. Someone with an emotional desire can cry about that bowl of rice all they want - even if it was their rice, the starving person is completely justified in enforcing their claim.

Even without need, humans still want things. It's built into us in the form of emotions. This is just human nature and a good moral system is built around our emotions.
However, letting emotional desire alone dictate who gets what would mean that all you have to get everything you want (even over the need or wants of others) would just be crying loud enough until you get it - and we are not small, spoiled children (or at least we shouldn't be). While need is an obvious reason for a claim (maintaining survival of a human being for example) emotional desire is more than just need. Emotional desire involves wanting things even if we don't necessarily need them. These kinds of claims are valid and reasonable (because even just wanting to survive is essentially just a desire in a human brain) - but without an actual need to compare, this type of claim is a different type of beast. A beast to be tamed using fairness. We “offset” a person's emotional desire for something by fairness.

For example, every kid at the table wants some of the tasty bacon. There is enough food for everyone, so everyone is going to survive, but the bacon specifically is limited (and coveted), so we need to set priorities beyond just the need to survive. So, assume a situation in which one kid didn't have any bacon yet while another wants a second portion of bacon. There's only one portion left, so whoever gets that last bit of bacon will be the last to get any bacon. Maximum fairness, in this situation, is achieved by letting the kid who didn't have any bacon at all yet have the last bit of bacon. That way, everyone had the same amount of bacon and nobody was “preferred” over anyone else.

This system alone may depict a fairly communist view of the world. And the fact that this is my personal belief system and that I agree with it may be a sign that I should also be in favor of Communism, which I may or may not be.¹⁾ Either way, while this system may be nice and fine on paper, it obviously won't play out quite as well in reality, mainly because of two things: Ownership and Physical Restrictions.

See the main page on Heinz Dilemma.

I respect, to a degree, the concept of ownership. I believe that ownership is not a physical, tangible thing - it's not a fact of reality - but a result of emotional processes in our brain. When acquiring a thing - no matter how - we tend to grow emotionally attached to it. Quite a lot, actually. I believe that this essentially amounts to a valid²⁾³⁾ Emotional Desire claim on that object. In a world where resources are limited, the loss of a thing potentially very damaging and acquiring a replacement very hard, this can create very strong emotional claims on things and is the reason why possession was legally (and morally) codified in the first place. Limitation, Damage and Reacquisition are the fundamental principles leading up to the concept of “ownership”: Breathing “someone else's air” doesn't exist as a tangible problem until air is scarce, the repercussions of running out of air severe (asphyxia, lethal) and reacquisition of air very difficult (think of a spaceship, for example).

Real world restrictions can influence our needs and desires, which in turn changes the strength of a claim. I live in a real world where I am restricted by laws and law enforcement in a way that requires me to adapt my perception and my emotional desire for things in accordance. For example, money is a rare resource that's hard to come buy for most, which means I need to acknowledge that, for most people, they have a very strong claim on the money they somehow did get (by going to work⁴⁾, for example). While I may not have signed up to live in a world where money dictates the movement of goods, other people live in that world and have emotions according to it. No matter how much I value money as a whole, the claim of another honest, hardworking person on their money is probably much stronger than mine, making stealing it immoral. In contrast, a grocery store chain that generates billions in profit each year, where resources are virtually unlimited, damage effectively nonexistent and reacquisition already secured years into advance⁵⁾, creates what's best described as a PIMO: Physically In, Mentally Out. While law enforcement forces me to acquire whatever objects I desire with money (even if I have a physical need, not just emotional desire!), I will philosophically disagree with that arrangement and be very inclined to circumvent whatever enforcement measures the law or, in this case, the grocery store chain have implemented. This is why store theft is a mass phenomenon, too. This is how it comes to be that I then also respect smaller stores, like family businesses, where resources are limited, where damage is severe and reacquisition is very hard.

See the main page on Moral Contract.

At any point in time, a person can consent to forfeit, fully or partially, their claim on a thing. Important: The consent part - every affected party must be aware of and consenting to such a Moral Contract. Renouncing a claim, for example when gifting a relative money, may or may not come with conditions or restrictions (for example: “I gift you 500 bucks, but I want you to invest it into your college tuition”). At this point the gifting person is renouncing their claim on the money, but only on the condition that the beneficiary use it for their tuition payments. Using it for something else would break the moral contract and therefore be immoral (unless a priority claim can be substantiated that justifies using the money for something else - an immediate need, for example).

Many of these moral contracts involve some implicit social expectations. The person forfeiting a claim is often thought of not completely giving up that claim. There is always a slight expectation, though not always explicitly stated, that they can recall the moral contract. People may view this more or less “wrong” depending on the circumstances, but the point is that these moral contracts agreed upon between people are often more involved than what is explicitly communicated, founded on an underlying foundation of morals most people assume to be in common agreement with and not necessary to state explicitly. For example, taking back a gift because they found out that they ended up needing it (“it”, for example money) more. While the beneficiary may feel bad about it, they will, at least to a degree, usually respect the claim the gifting person has on that money.