Ibn Taymiyyah, may Allah have mercy on him, interprets the balance as sound analogical deduction, justice, and the thing that is used for measuring weight. He says,
“He, the Almighty, revealed that He sent down the Book and the Balance. Many righteous predecessors suggest that the balance is intended to mean justice. They said that the balance refers to the scale that is used for measuring weight, and it means justice. The Almighty revealed that the purpose of sending down the balance is to make people uphold justice. This means that the Almighty made the balance part of human nature, so that they know what justice entails. This includes the ability to distinguish between parties and to resolve conflicts and contradictions.”
Ibn Taymiyyah added,
“Since the Book and the Balance were sent down, they can never contradict each other. Elements of authentic texts can never contradict elements of sound reason and judgement as derived from the balance."
Ibn al-Qayyim, may Allah have mercy on him, says, “Since the Quran is consistent and sound, elements of sound balance can never contradict each other.”
Ibn Taymiyyah, may Allah have mercy on him, says,
“Most exegetes believe that the balance means justice because it was sent down along with the Book. Mujahid, may Allah have mercy on him, says, ‘The balance means the scale used for measuring weight, yet the other view is also valid. Justice and the ability to recognize what justice entails are instilled in human nature.’”
Ibn Taymiyyah suggests that the Almighty instils the balance in the hearts of His obedient servants, and the evidence for this is the Hadith in which the Prophet ﷺ said, “And whoever patiently awaits the fulfilment of what he wishes, an angel will be sent by Allah to guide him.”
In this regard, al-Bukhari and Muslim, in their two respective Collections of Hadiths, narrated that Hudhaifa said, “Honesty originally descended into the deepest recesses of the hearts of people. Then the Qur'an was revealed, and they learned it from the Qur'an, and they learnt from the Sunnah.”
In his attempt to refute the Zahirites’ claim, Ibn Taymiyyah explains that the approach of this Islamic school is based on many misconceptions because they do not understand the concept of the balance. He says, “They rely on superficial readings of texts, and they ignore the deeper meanings. Consequently, they do not understand the Holy Quran, and they do not understand the concept of the balance.”
I believe that interpreting the balance as it is mentioned in the chapter of al-Hadid as justice sounds reasonable. This is because the Almighty explains that the purpose of the balance is upholding justice and equality. However, interpreting the balance as analogical deduction sounds unreasonable because Allah associates justice with the Book and the balance. Accordingly, the balance cannot mean analogical deduction, for justice entails following all the elements of the Book, rather than analogical deduction alone. Furthermore, interpreting the balance as independent reasoning is invalid because the Book and the Balance were sent down together, and independent reasoning constitutes just one of many ways of establishing evidence for an Islamic ruling.
However, Ibn Taymiyyah’s saying that the balance is instilled in the hearts of Allah’s righteous servants provides a valuable insight, and I may add that the balance can be understood by those with a righteous nature and sound reason.
 Cited in Jami’ al-Masa’il, Ibn Taymiyyah, investigated by Muhammad Aziz Shams, Dar A’lam al-Fawa’id, 1424 H (vol.2, p. 257 -258).
 Cited in ‘Ilam al-Muwaqq’in (vol.1, p.33).
 Cited in Majmu’ al-Fatawa (vol.12m p.2249, vol.35, p.366).
 Cited in Abu Dawod’s Kitab Alaqdiyah - Chapter on “Looking forward to Quick Fulfilment of Wishes”, Hadith No. (3578).
 Cited in Sahih al-Bukhari (vol. 11, p.333), Hadith No. 6497, 7086, and in Sahih Muslim, Hadith No. 143.
 Jami’ al-Masa’il (vol.2, p.282).