He is asking how he can be truly just in all things

Firstly: 

It is good to see among people one who loves to be just and is eager to do so, and is asking for more details and how to achieve that. It is by virtue of justice that the heavens and the earth are maintained, and justice is the foundation on which the best interests of people and countries may be served. It is one of the most important things that Allah has enjoined in His holy Book. Allah, may He be glorified and exalted, says (interpretation of the meaning):

“Verily, Allah enjoins Al-‘Adl (i.e. justice and worshipping none but Allah Alone – Islamic Monotheism) and Al-Ihsan (i.e. to be patient in performing your duties to Allah, totally for Allah’s sake and in accordance with the Sunnah (legal ways) of the Prophet SAW in a perfect manner), and giving (help) to kith and kin (i.e. all that Allah has ordered you to give them e.g., wealth, visiting, looking after them, or any other kind of help, etc.): and forbids Al-Fahsha (i.e all evil deeds, e.g. illegal sexual acts, disobedience of parents, polytheism, to tell lies, to give false witness, to kill a life without right, etc.), and Al-Munkar (i.e all that is prohibited by Islamic law: polytheism of every kind, disbelief and every kind of evil deeds, etc.), and Al-Baghy (i.e. all kinds of oppression), He admonishes you, that you may take heed.”

[an-Nahl 16:90]

“Verily! Allah commands that you should render back the trusts to those, to whom they are due; and that when you judge between men, you judge with justice. Verily, how excellent is the teaching which He (Allah) gives you! Truly, Allah is Ever All-Hearer, All-Seer.”

[an-Nisa’ 4:58]. 

The shar‘i principle that is based on the mercy of Allah, may He be exalted, and His will to make things easier for people, dictate that the Muslim should obey whatever he can of these commands. So he should attain justice in his own life, deal with the people around him on the basis of justice, and interact with all other creatures on that basis; all of that should be in accordance with what he is able to do, for absolute justice belongs only to Allah, may He be glorified and exalted. 

Hence when Allah, may He be exalted, enjoined fairness and giving full weight and measure – which is a type of justice – He followed that with a statement that there is no blame attached to that which is beyond one’s capability. Allah, may He be glorified and exalted, says (interpretation of the meaning):

“and give full measure and full weight with justice. We burden not any person, but that which he can bear. And whenever you give your word (i.e. judge between men or give evidence, etc.), say the truth even if a near relative is concerned, and fulfill the Covenant of Allah, This He commands you, that you may remember”

[al-An‘aam 6:152]. 

It says in Mafaateeh al-Ghayb by ar-Raazi (13/180): 

It should be noted that because it is possible that someone may think that it is obligatory to fulfil the command to the highest degree – which is very difficult when it comes to justice – Allah, may He be exalted, followed that with something that spares us this difficulty, as He says: “We burden not any person, but that which he can bear.” End quote. 

Al-‘Allaamah as-Sa‘di (may Allah have mercy on him) said: 

“and give full measure and full weight with justice” means doing so fairly, faithfully and completely. If you strive hard to do that, then “We burden not any person, but that which he can bear” that is, only as much as he is able to bear, without causing him undue difficulty. If a person is keen to give full weight and measure, then some shortcoming occurs without any negligence on his part and without him realizing it, then Allah is Pardoning and Oft-Forgiving. From this verse and similar verses the scholars of usool determined that Allah does not give anyone a burden greater than he can bear, and in the case of one who fears Allah with regard to what He has commanded, and has done all that he is able to in that regard, there is no blame on him for anything other than that.

End quote from Tayseer al-Kareem al-Mannaan, p. 280 

Al-‘Allaamah Muhammad Rasheed Rida (may Allah have mercy on him) said: 

“We burden not any person, but that which he can bear” – this is a new sentence which explains the ruling concerning the difficulties that may be faced by people of piety and religious commitment when they are trying to be fair in measures and weights, because being fair is something very subtle that cannot be achieved every time you measure or weigh out something, unless you use scales such as those used for weighing gold, which gives the weight to the accuracy of one gram or less. To commit oneself to achieving that level of accuracy when buying grains or produce is very difficult. This is a matter that may arise in the mind of the pious person; he may wonder what the ruling is (i.e., how accurate must one be?). The answer to that question came in this verse: Allah does not burden any person but that which he can bear, so that there will be no great pressure or hardship in seeking to achieve something that is very difficult. Therefore Allah did not burden the one who buys and sells the foods mentioned above, and similar items, by requiring him to weigh or measure to the accuracy of one gram. Rather Allah instructs him to be fair and just when weighing and measuring, whether he is doing it for himself or to give to others, according to what is customary, so that he will be certain that he is not being unfair by giving more or less than that which is regarded as fair according to custom. 

The principle of making things easy and keeping the burden within the limits that a person could bear – which dictates waiving anything that could cause undue hardship or difficulty – is one of the strongest foundations of this sharee‘ah, which is based on the foundation of truth and justice; there is no set of man-made laws that could equal it. If the Muslims acted in accordance with this principle, then their dealings and transactions would become proper and would flow smoothly, which would create trust and honesty among them, and they would offer an example for cheaters and corrupt people to learn from. Their affairs would not have become corrupted and they would not have lost trust among themselves, which was replaced with trust of the foreigners who are aiming to control and dominate them, which is what happened when they abandoned these principles and guidelines. As a result you now see some ignorant apostates spouting nonsense and saying ‘our religion is the cause of our backwardness and that led to others going ahead of us.’

End quote from Tafseer al-Manaar, 8/168 

Our advice to you is to do your best to achieve justice in all areas of your life. So be fair to yourself by focusing on that which will lead to salvation and victory in the hereafter; avoid that which will cause you to slip and fall short, so that you will not expose yourself to punishment. Be just towards other people by upholding ties of kinship, treating people kindly and pardoning those who mistreat you; love for them what you love for yourself of good. Be just towards plants, animals and the earth by showing mercy and compassion, and avoid causing harm. Then if Allah sees you doing this, He will reward you by His leave as He, may He be glorified and exalted, says (interpretation of the meaning): “Is there any reward for good other than good? Then which of the Blessings of your Lord will you both (jinns and men) deny?” [ar-Rahmaan 55:60-61]. 

Secondly: 

With regard to the hadeeth mentioned in the question, it does not have any saheeh isnaad (sound chain of narrators) from the Prophet (blessings and peace of Allah be upon him) and it was not narrated by any of the authors of the famous books of hadeeth. Rather it was mentioned by al-Muttaqi al-Hindi in his book Kanz al-‘Ummaal (16/127) where he said: 

Shaykh Jalaal ad-Deen as-Suyooti (may Allah have mercy on him) said: I found in the handwriting of Shaykh Shams ad-Deen ibn al-Qammaah in a collection of his, (a narration) from Abu’l-Abbaas al-Mustaghfiri: I went to Egypt, intending to seek knowledge from Imam Abu Haamid al-Masri, and I asked him about the hadeeth of Khaalid ibn al-Waleed. He told me to fast for one year, then I asked him again about (that hadeeth). Then he told me its isnaad (chain of narration) from his shaykhs, going back to Khaalid ibn al-Waleed, who said: A man came to the Prophet (blessings and peace of Allah be upon him) and said: I am going to ask you about what will happen in this world and the hereafter. He said to him: “Ask about whatever you like.” … And among the things he asked was: I want to be the most just of people. He said: “Love for people what you love for yourself; you will be the most just of people.” End quote. 

This – as you can see – is not sufficient to prove that this hadeeth is sound, because the names of the chain of narration going back to Khaalid ibn al-Waleed (may Allah be pleased with him) are not mentioned. 

It says in Fataawa al-Lajnah ad-Daa’imah (4/454): 

This hadeeth is not saheeh because there are unknown narrators in its isnaad. End quote. 

‘Abd al-‘Azeez ibn Baaz, ‘Abd ar-Razzaak ‘Afeefi, ‘Abdullah ibn Ghadyaan 

Shaykh Ibn Baaz (may Allah have mercy on him) said: 

This hadeeth is fabricated and its narrators are unknown. It is as if the one who fabricated it compiled its text from saheeh hadeeths and the words of some of the scholars, and some of its phrases are odd and are not in harmony with shar‘i evidence. Undoubtedly the correct view with regard to the matters mentioned in this hadeeth is that which is indicated by the saheeh hadeeths; as for this text, it cannot be relied upon or quoted as evidence, because it does not have a saheeh isnaad.

End quote from Majmoo‘ Fataawa Ibn Baaz, 26/326 

There is a sentence in this fabricated hadeeth, that is proven in the saheeh report according to which the Prophet (blessings and peace of Allah be upon him) said: “Love for other people what you love for yourself, (then) you will be a Muslim.”

Narrated by Ahmad in al-Musnad, 13/459; classed as saheeh by al-Albaani in as-Silsilah as-Saheehah, no. 930. 

It was also narrated from Anas ibn Maalik (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “No one of you (truly) believes until he loves for his brother what he loves for himself.”

Narrated by al-Bukhaari (13) and Muslim (45). 

And Allah knows best.