The Messenger of Allah (sal Allahu alaihi wa sallam) said, “The Balance will be set up on the Day of Resurrection, and even if the heavens and the earth were to be weighed in it, they would fit. The angels will say, ‘O Lord! Who will be weighed in this?’ Allah will say, ‘Whoever I will among My creation.’ The angels will say, ‘Glory be to You. We did not worship You as You deserved to be worshipped.’”
[Al-Hakim - Classed as Sahih by Sh al-Albaani]
The Balance is a real scale in which the deeds of the people will be weighed. It is a precise scale, which does not give any discrepancy, whether more or less, in its measurements.
Allah says (interpretation of the meaning): And We shall set up balances of justice on the Day of Resurrection, then none will be dealt with unjustly in anything. And if there be the weight of a mustard seed, We will bring it. And Sufficient are We as Reckoners. [Al-Anbiya 21:47]
The Scholars (may Allah have mercy upon them) said: “When the Reckoning is completed, the deeds will be weighed. The Reckoning will be an evaluation of peoples deeds, then the weighing will be to determine their value so that reward or punishment may be awarded accordingly.”
Allah says (interpretation of the meaning): Then, those whose scales (of good deeds) are heavy, they are the successful. And those whose scales (of good deeds) are light, they are those who lose their own selves, in Hell will they abide. [Al-Mu'minun 23:102-103]
Allah also says (interpretation of the meaning): Then as for him whose balance (of good deeds) will be heavy, He will live a pleasant life (in Paradise).
But as for him whose balance (of good deeds) will be light, He will have his home in Haawiyah (i.e. pit in Hell). And what will make you know what it is? (It is) a hot blazing Fire! [Al-Qari'ah 99:6-11]
And Allah knows best!