In Bereshis 4:8 we read: וַיֹּאמֶר קַיִן, אֶל-הֶבֶל אָחִיו; וַיְהִי בִּהְיוֹתָם בַּשָּׂדֶה, וַיָּקָם קַיִן אֶל-הֶבֶל אָחִיו וַיַּהַרְגֵהוּ
And Cain spoke unto Abel his brother. And it came to pass, when they were in the field, that Cain rose up against Abel his brother, and slew him.
Why did Kayin do this? I recall learning that they argued over a who was able to marry a second twin sister. I'm not sure what the source of this is but it seems to me a rather empty reason for murder.
The reason you mention is one on the list in Bereishis Rabba 22 And Cain spoke to Abel his brother. And it came to pass when they were in the field... " (Gen 4:8) What were they fighting about? They said, "Let's divide up the world." One took the earth and one took the moveable objects. One said "That land that you are standing on is mine!" and the other said "What you are wearing is mine!" One said "Take it off!" and the other said "Fly!" Because of this, "Cain rose up against Abel his brother and slew him. Rabbi Joshua of Sikhnin in the name of Rabbi Levi said: they each took earth and each took moveable objects. And what were they fighting about? One said, "The Temple will be built in my territory!" and the other said "The Temple will be built in my territory!" as it is written "when they were in the field"-- and "field" can refer only to the Temple, hence what is written: "Zion shall be threshed as a field" (Micah 3). And because of this, "Cain rose up against Abel his brother." Judah bar Ami said: they were fighting about Primordial Eve. Rabbi Eivo said: Primordial Eve had already died. And what were they fighting about? Rabbi Huna said: A[n extra]‡ twin girl was born along with Abel. One said, "I will take her, because I am the firstborn." And the other said, "I will take her because she was born with me."
‡Safaria forgot to put this into their translation.
Haamek Davar (see his commentary to the whole section for context) explains as follows. Abel was dependent on the farmer Cain for the staple, bread; thus, Cain was allowed to work him as needed and even to hit him in the course of training him to work properly. And that's what happened — except that he hit him until he died. Now, based on that relationship alone, he was not liable for the mortal blow. God's complaint to Cain for the death was based only on the fact that they were brothers and so Cain should have gone beyond the master-servant relationship.
Kayin killed Hevel because his offering was not accepted from G-D, but Hevel's was so he was jealous.
The Targum Yerushalmi (on bereishis 4:8) brings that they had a controversy on justice, the reward given to the righteous, and the world to come. Kayin said that the there was no justice in the world, or the world to come, there was no good reward given to the righteous nor vengeance be taken of the wicked. Hevel said the opposite, saying that there is justice in the world, there is reward to the righteous and because of this his offering had been accepted and that of Kayin had not. Seeing that this argument had become not merely philosophical but personal, Kayin attacked Hevel and Killed him.
In addition to what @user6591 wrote about Kayin wanting to take Hevel's twin sister, the Pirkei DeRabbi Eliezer 21:7 elaborates and writes:
Rabbi Zadok said: A great hatred entered Cain's heart against his brother Abel, because his offering had been accepted. Not only (on this account), but also because Abel's twin-sister was the most beautiful of women, and he desired her in his heart. Moreover he said: I will slay Abel my brother, and I will take his twin-sister from him, as it is said, "And it came to pass when they were in the field" (Gen. 4:8). "In the field" means woman, who is compared to a field. (Sefaria translation)
So we see that he was jealous not only of Hevel's sacrifice gaining acceptance but also because he was jealous of him for marrying his sister whom he coveted.
The Targum Yonasan, Bereishis 4:8 provides a clearer reasoning on what this jealousy about Hevel's sacrifice gaining acceptance was predicated on:
And Cain said to Abel his brother, Come, and let us two go forth into the field. And it was that when they two had gone forth into the field, Cain answered and said to Abel, I perceive that the world was created in goodness, but it is not governed (or conducted) according to the fruit of good works, for there is respect to persons in judgment; therefore it is that thy offering was accepted, and mine not accepted with good will. Abel answered and said to Cain, In goodness was the world created, and according to the fruit of good works is it governed; and there is no respect of persons in judgment; but because the fruits of my works were better than thine, my oblation, before thine, hath been accepted with good will. Cain answered and said to Abel, There is neither judgment nor Judge, nor another world; nor will good reward be given to the righteous, nor vengeance be taken of the wicked. And Abel answered and said to Cain, There is a judgment, and there is a Judge; and there is another world, and a good reward given to the righteous, and vengeance taken of the wicked. And because of these words they had contention upon the face of the field; and Cain arose against Abel his brother, and drove a stone into his forehead, and killed him. (Sefaria translation my emphasis)
So it would seem that the heart of this jealousy was based on a deeper more profound (albeit incorrect) outlook of the running of the world. Kayin saw Hevel's 'winning' sacrifice as an example of Divine favouritism which he wasn't able to 'get over'. It was this intense jealousy that drove him to lash out so violently.
