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.