Seven, as in Revelation 15:1, signifies everything in an universal sense. The number 'seven' was considered holy, as is well known, because of the six days of creation, and the seventh, which is the celestial self, where peace, rest, and the Sabbath is. The number seven occurs so frequently in the rites of the Jewish church and is held holy everywhere.

So times were divided into seven, longer and shorter intervals, and were called weeks, like the great intervals of times till the coming of the Messiah, in Daniel 9:24-25. The time of seven years is called 'a week' by Laban and Jacob, as in Genesis 29:27-28. So wherever the number seven occurs, it is considered holy and sacred, as in Psalm 119:164, and in Isaiah 30:26.

As the periods of a person's regeneration are distinguished into six, prior to the seventh, or the celestial self, so the times of vastation are also distinguished, until nothing celestial is left. This was represented by the many captivities of the Jews, and by the last Babylonian captivity, which lasted seven decades, or seventy years. This was also represented by Nebuchadnezzar, in Daniel 4:16, 22, 29. It also refers to the vastation of the end times, in Revelation 15:1, 7-8. They should 'tread the holy city under foot, forty and two months, or six times seven,' as in Revelation 11:2 and Revelation 5:1. So the severity and increments of punishment were expressed by the number seven, as in Leviticus 26:18, 21, 24, 28 and Psalm 79:12.

(Riferimenti: Apocalypse Explained 5, 7-8, 15; Arcana Coelestia 395; Daniel 9, 9:24, 9:25; Psalms 119)

395. 'Anyone killing Cain, vengeance will be taken on him sevenfold' means that to violate faith thus separated was utterly forbidden. This is clear from the meaning of 'Cain' as separated faith, and from the meaning of 'seven' as utterly inviolable. As is well known, the number seven was considered holy on account of the six days of creation and of the seventh, which is the celestial man in whom peace, rest, and the Sabbath exist. This is the reason why the number seven occurs so many times in the religious ceremonies of the Jewish Church, in every instance standing for that which is holy. It is also the reason why periods of time, long as well as short, were divided into seven, and were called weeks, as in the case of the long time intervals leading up to the time when the Messiah was to come, Daniel 9:24-25. A period of seven years is also called a week by Laban and Jacob, Genesis 29:27-28. Consequently wherever the number seven occurs it stands either for something holy or else for something utterly inviolable, as in David,

Seven times in the day I praise You. Psalms 119:164.

In Isaiah,

The light of the moon will be as the light of the sun, and the light of the sun will be sevenfold, as the light of seven days. Isaiah 30:26.

Here 'the sun' is love, and 'the moon' faith deriving from love, a faith which is to be as love.

[2] Just as the periods of man's regeneration divide into six before he reaches the seventh, which is the celestial man, so also do the periods of vastation even until nothing celestial is left. This was represented by the many captivities of the Jews, and by the last of them, the Babylonian, which was a captivity of seven decades, that is, seventy years. And it was several times stated that the land had to rest during its Sabbaths. It was also represented by Nebuchadnezzar, of whom it is said in Daniel,

His heart will be changed from man, and the heart of a beast given him until seven times will pass over him. Daniel 4:16, 25, 32.

In reference to the vastation of the last times it is recorded in John,

I saw another sign in heaven, great and wonderful - seven angels holding the seven Revelation 15:1, 6-7.

They will trample over the holy city for forty-two months (that is, six times seven). Revelation 11:2.

In the same book,

I saw a book [written] within and on the back, sealed with seven seals. Revelation 5:1.

Severe and increased penalties were for the same reason expressed by the number seven, as in Moses,

If you will not obey Me in this matter, I will chastise you seven times worse for your sins. Leviticus 26:18, 21, 24, 28.

In David,

Return to our neighbours sevenfold into their bosom. Psalms 79:12.

So then, it is because it was utterly forbidden to violate faith - since it had a use to serve, as has been stated - that the statement is made about 'vengeance being taken sevenfold on him who killed Cain'.