I agree with Muslims on this point. Though I may differ slightly. As far as I know, Muslim's believe that there is a tally system of sorts which God uses to judge our righteousness. This means that a man can't know whether he is in right standing with God, he must wait until the day of judgement.
The Hebrew scriptures do NOT teach that there is a tally system. If an evil man turns from his evil and follows God's commandments then it says his evil deeds are ERASED. This means that they are not being weighed against each other.
21But if the wicked will turn from all his sins that he hath committed, and keep all my statutes, and do that which is lawful and right, he shall surely live, he shall not die.
22All his transgressions that he hath committed, they shall not be mentioned unto him: in his righteousness that he hath done he shall live…Ezekiel 18: 21-22
Please correct me if I am wrong about Islamic views of God's judgement.
It is true that people can't know for sure at their lives if they will be going to heaven or hell. The point of this is to have people trying to be righteous all the time. The main concern also would be they you never know how one could go astray and be doing a sin and suddenly die on that sin. So we have always to strive to be close to Allah and be righteous. However that is not all, we have to look at the other side also.
Allah gives you assurances in the Quraan,
18:30 Indeed, those who have believed and done righteous deeds - indeed, We will not allow to be lost the reward of any who did well in deeds.
2:112 Yes [on the contrary], whoever submits his face in Islam to Allah while being a doer of good will have his reward with his Lord. And no fear will there be concerning them, nor will they grieve.
2:261 The example of those who spend their wealth in the way of Allah is like a seed [of grain] which grows seven spikes; in each spike is a hundred grains. And Allah multiplies [His reward] for whom He wills. And Allah is all-Encompassing and Knowing.
2:277 Indeed, those who believe and do righteous deeds and establish prayer and give zakah will have their reward with their Lord, and there will be no fear concerning them, nor will they grieve.
4:40 Indeed, Allah does not do injustice, [even] as much as an atom's weight; while if there is a good deed, He multiplies it and gives from Himself a great reward.
As for one who sins against God, there are many things we must know about that. First thing we should know that in Islam, when one embraces it, all his sins are forgiven and he will be like a new born without sins.
Second, there is repentance in Islam which erases the sin. How does one repent?
Repentance grants us forgiveness.
But what is the meaning to repent?
1-To be true about it.
2- Stop doing it again.
3- You have to regret it. Like you don't say I used to steal ,,,, wow they were good old days. You have to regret doing it.
4- Decide not to go back to the same sin in the future
5- If you can return the rights to people you have done damage do, you should
Also here are other references from the Quraan.
Do not despair of God's mercy; He will forgive you of all your sins".Qur'an (39:53).
"Except those who repent, have faith and good deeds, those Allah will charge their sins for good deeds. Certainly Allah is most forgiving and merciful." (Qur'an 25:70)
This is a greatest glad tiding for those who repent and combine their repentance with deep faith and good deeds.
Repentance breeds good deeds, whilst sinning (without repentance) can cause deprivation of obedience altogether. It has been said that committing sins regularly will darken and harden the heart and make purifying it once again a difficult mission. It may even lead a person to reject Allah completely (Allah forbid) or lead him to commit a bigger sin. There is no recourse for a sinner except to ask Allah for forgiveness and to feel great regret for his actions.
Repentance is to repent from the heart, to train the heart into obedi ence and to make a firm resolution never to commit the sin again.
Abu Bakr Al siddiq (May Allah be pleased with him), narrated:
"I heard Prophet Mohammad (PBUH) saying: ‘There isn’t a man who, when he commits a sin, rises, makes ablution, and offers two rak'as of prayers, but Allah forgives his sins.’
Allah says in the Qur'an:
"Those (are the true believers) who, when they commit an evil deed, or wrong their souls, remember Allah, and seek forgiveness for their sins - and who but Allah forgives sins? They do not insist upon the sins they have committed, and they know (that Allah is forgiving)." (Qur'an 3:135)
Abu Dharr reported: The Messenger of Allah, peace and blessings be upon him, said:
Fear Allah wherever you are, follow a bad deed with a good deed and it will erase it, and behave with good character toward the people.
So as you see Islam doesn't teach that there is a point where you can safely say ok now I am going to heaven. However there are many ways one would be forgiven for his sins. So yes it is as you described as weighing deeds against each other but there are many ways in Islam where if you truly do it, sins would be forgiven.
I wish that answers the questions.