Giving everything its due value is Justice.
The word Haqq in Arabic denotes justice in giving the due importance and regard to people and things and the greatest Haqq is to give the Creator His credit by worshipping Him alone without associating partners.
Huququllaah and Huququl Ibad are the terms used to represent the rights of God and the Rights of people respectively.
The opposite is Zulm. When we don't give people or things their due rights or value and when we don't put things in their due places it is called zulm or Injustice. Every living being has its value.
Not giving the Haqq is Zulm.
Huququllah or the Rights of the Creator
Unless and until we acknowledge, understand and have firm belief in the Oneness of God and His Supremacy we can never realize how He should be obeyed and how he should be feared. The creatures have the obligation to know Who created them, where they have come from and to where they belong. They have the obligation to know and believe in the Creator and Worship Him as He should be worshiped.
In Chapter 2 Ayah 102 Allah says:
O you who have believed, fear Allah as He should be feared and do not die except as Muslims [in submission to Him].
This is not for Allah, rather it is we who benefit in this world and would benefit greatly in the Hereafter if we give our Creator His right to be worshipped and obeyed.
A Muslim or a person who has submitted his or her will to the Will of Allah has achieved the status of a believer and he enjoys the fruits of Iman in both the worlds. The ultimate aim or success for him is nothing but the Pleasure of Allah.
The ultimate objective of a true Muslim is to gain Divine pleasure and attain success on the Day of Judgment. For achieving this objective we get detailed guidance from Qur’an and Sunnah regarding our religious obligations, which may be described with reference to the following three important terms: (1) Personal enslavement to God, (2) Acting as witnesses unto all of mankind, and (3) Establishing the system of social justice of Islam. We have clearly spelled out the pre-requisites of these duties at length.Dr Israr Ahmad in The Obligations to God
This is an amazing topic and one can write on and on about the Greatness of Allah and His blessings and Mercy to all His creatures whether they are believers or not. Allah guides Whom He wills and those who fulfill their rights as Muslims hope and pray for the True Success that is promised by their Lord.
Huququl Ibaad or the Rights of the people
Apart from Huququllah, a believer is also required to fulfill the rights of his near relatives, neighbours etc. These are called Huququl Ibaad which are based on Justice and morality. Among them the parents are the most important people. A mother has great rights in Islam and there are numerous verses and Ahadith to back this obligation.
This does not complete the whole picture but...
the others who are entitled to be taken care of and given due value are the blood relatives.
Among them we can count our own siblings, to cousins and other relatives.
Allah wants us to be kind to them and to give them due respect and importance.
In some verses where the Muhajireen and Ansaar are mentioned and the law of inheritance was being discussed Allah mentions the importance of blood relatives and their right of inheritance.
And those who believed afterwards, and emigrated and strove hard along with you, (in the Cause of Allah) they are of you. But kindred by blood are nearer to one another regarding inheritance in the decree ordained by Allah. Verily, Allah is the All-Knower of everything.
Surah Anfal 75
The blood relatives (mother, father, brothers, sisters etc.) therefore, have a relationship that is acknowledged by the Creator Himself and it should by no means be belittled by anyone. The life and practice of Muhammad ﷺ tells us that the elders should be respected, the younger ones should be dealt with mercy and care and they should all support each other by all means.
It is indeed not giving Haqq when someone gives preference to other distant relatives over the nearest relatives. This is something which is against the simple logic as well as the moral obligation as dictated by our beautiful and Just religion Islam.
Islam is based on Truth and Justice and this is what it requires us to do as wise and informed believers who take their notes from the Quran and Sunnah; these being the constant Guide and teachers in our life.
To conclude, the only thing to be kept in mind while giving everyone and everything its due and its Haqq we must first realize its importance and place in our life. For example we are required to love Allah above anyone and anything else. After Him is the Messenger of Allah Muhammad ﷺ who should be given preference over everyone and even our own selves.
Under this category of obligation we can have people ranging from our near relatives to those who are absolutely unrelated like the poor people, the orphans, the wayfarer, the traveller, the companions and the neighbours. We have to give each of them their due rights and have a clear understanding of what our duties toward them are.
Consequently, a person is required to give the people in his life importance which is due unto them. This is the way to maintain a balance in our worldly life as a whole and to ensure that we get our due reward in the Hereafter inshaAllah!
Give everybody his right and everything will be all right.