How Books of Deeds Will Be Distributed
Question

How will the books of people’s deeds be distributed to the people on the Day of Resurrection? How will their deeds be weighed?
Praise be to Allah.Distribution of the books of deeds on the Day of Judgement
When people have been brought to account for their deeds, each person will be given their book that contains the record of all his deeds. The believer will be given his book in his right hand, as a sign of honour. He will be the one who is saved and happy on the Day of Resurrection. Allah says (interpretation of the meaning): 
“Then as for him who will be given his Record in his right hand, He surely, will receive an easy reckoning, And will return to his family in joy!” [Al-Inshiqaq 84:7-9] 
“Then as for him who will be given his Record in his right hand will say: ‘Here! Read my Record! Surely, I did believe that I shall meet my Account!’ So he shall be in a life, well-pleasing. In a lofty Paradise, The fruits in bunches whereof will be low and near at hand. Eat and drink at ease for that which you have sent on before you in days past!” [Al-Haqqah 69:19-24]
But the disbelievers, hypocrites and followers of misguidance will be given their books in their left hands , from behind their backs. Allah says (interpretation of the meaning): 
“But whosoever is given his Record behind his back, He will invoke (for his) destruction,
And he shall enter a blazing Fire” [Al-Inshiqaq 84:10-12] 
“But as for him who will be given his Record in his left hand, will say: ‘I wish that I had not been given my Record! And that I had never known how my Account is! Would that it had been my end (death)! My wealth has not availed me; My power (and arguments to defend myself) have gone from me!’ (It will be said): ‘Seize him and fetter him; Then throw him in the blazing Fire. Then fasten him with a chain whereof the length is seventy cubits!’” [Al-Haqqah 69:25-32]
When the people have been given their books, it will be said to them: 
“This Our Record speaks about you with truth. Verily, We were recording what you used to do (i.e. Our angels used to record your deeds).” [Al-Jathiyah 45:29] 
“Read your book. You yourself are sufficient as a reckoner against you this Day.” [Al-Isra 17:14]
The Balance of weighing deeds
The Balance will be set up to weigh people’s deeds . Al-Qurtubi said: “When the Reckoning is completed, then people’s deeds will be weighed, because the weighing has to do with reward and punishment. So it is apt that it should come after the Reckoning. The Reckoning is to evaluate the deeds, and the weighing is to determine the amount of reward or punishment.” 
The texts indicate that the Balance is a real Balance, with two pans, in which people’s deeds will be weighed. It is a huge Balance, the size of which is known only to Allah. The scholars differed as to whether it is one Balance in which people’s deeds will be weighed, or whether there are numerous Balances, so that each person will have his own Balance. Those who said that there will be numerous balances quote as evidence the fact that the word appears in plural form in some verses, for example (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 to take account.” [Al-Anbiya 21:47]
Those who say that it will be one Balance quote as evidence the words of the Prophet (peace and blessings of Allah be upon him): “The Balance will be set up on the Day of Resurrection, and if the heavens and the earth were to be weighed in it, it would be sufficient to carry them. And the angels will say, ‘O Lord, who is this for?’ Allah will say, ‘For whomsoever I will from among My slaves.’” (al-Silsilat al-Sahihah, 941). They interpret the verse in which the plural form is mentioned as referring to the large number of things to be weighed, namely words, deeds, records and people.  
Weighing words on the Day of Judgement
One of the things that indicate that words will also be weighed is the hadith narrated by Abu Hurayrah, according to which the Prophet (peace and blessings of Allah be upon him) said: “Two words which are light on the tongue but will weigh heavily in the Balance and are beloved to the Most Merciful: Subhan Allah il-‘Azim, Subhan Allahi wa bi Hamdihi (Glory be to Allah the Almighty, Glory and praise be to Allah).” (Narrated by al-Bukhari, 6406) 
Weighing deeds on the Day of Judgement
The fact that deeds will be weighed is indicated by the sahih hadith narrated from Abu’l-Darda who said: “I heard the Prophet (peace and blessings of Allah be upon him) say, ‘There is nothing that will be placed in the Balance that will weigh more heavily than a good attitude. The one who has a good attitude will attain thereby the status of one who fasts and prays (a great deal).’” (Sahih Sunan al-Tirmidhi, 1629) 
Weighing books of deeds on the Day of Judgement
Another thing that indicates that the books of deeds will be weighed is the hadith of al-Bitaqah from ‘Abd-Allah ibn ‘Amr ibn al-‘As who said, the Messenger of Allah (peace and blessings of Allah be upon him) said: “Allah will separate a man belonging to my ummah in the presence of all creatures and will spread ninety-nine scrolls for him, each scroll extending as far as the eye can see. Then He will say, ‘Do you object to anything in this? Have my scribes who keep note wronged you?’ He will say, ‘No, my Lord.’ He will ask him, ‘Do you have any excuse?’ He will say, ‘No my Lord.’ Allah will say, ‘On the contrary, you have with Us a good deed , and you will not be wronged this Day.’ A slip of paper will then be brought out, on which are the words ‘Ashhadu an la ilaha ill-Allah wa ashhadu anna Muhammadan ‘abduhu wa rasuluhu  (I  bear witness that there is no god but Allah, and I bear witness that Muhammad is His slave and His Messenger).’ Allah will say, ‘Bring your weight (i.e., the scrolls).’ The man will say, ‘O Lord, what is this slip of paper in comparison to these scrolls?’ And He will reply, ‘You will not be wronged.’ The scrolls will then be put in one side of the Balance and the slip of paper in the other, and the scrolls will become light and the slip of paper heavy, for nothing could compare in weight to the name of Allah.” (Sahih Sunan al-Tirmidhi, 2127)  
Weighing people on the Day of Judgement
One of the things that indicate that people will be weighed is the hadith narrated from Abu Hurayrah (may Allah be pleased with him), according to which the Messenger of Allah (peace and blessings of Allah be upon him) said: “A huge fat man will be brought on the Day of Resurrection, and he will not weigh more before Allah than the wing of a gnat. Recite: ‘and on the Day of Resurrection, We shall assign no weight for them’ [Al-Kahf 18:105 – interpretation of the meaning].” (Narrated by al-Bukhari, 4729)
It is also indicated by the fact that Ibn Mas’ud was trying to break a siwak branch from an arak tree and he had thin legs and the wind started to buffet him, so the people laughed at him. The Messenger of Allah (peace and blessings of Allah be upon him) said, “What are you laughing at?” They said, “O Prophet of Allah, because his legs are so thin.” He said, “By the One in Whose Hand is my soul, they will weigh more heavily in the Balance than Mount Uhud.” Its isnad was classed as hasan by al-Albani in Sharh al-Tahhawiyyah, no. 571, p. 418
 We ask Allah to make us weigh heavily in the Balance.
And Allah knows best.