ויתן להם משה לבני-גד ולבני ראובן ולחצי שבט מנשה בן-יוסף את-ממלכת סיחן מלך האמרי ואת-ממלכת עוג מלך הבשן וגו’
Moshe gave to the children of Gad, the children of Reuven, and to half the tribe of Menashe the son of Yosef the kingdom of Sichon, the King of the Amorites, and the kingdom of Og, the king of Bashan…
After the defeat of Sichon and Og, the Jewish people had conquered a large amount of land to the east of the Jordan River. The tribes of Reuven and Gad requested that instead of acquiring a portion of the land of Israel proper, they wanted this conquered land to be divided amongst them. After swearing that they’d help their brethren conquer the land of Israel, Moshe agreed to their request. The Torah tells us that Moshe gave them the land, as well as some of the tribe of Menashe. Why did Moshe give part of Menashe as well, when we aren’t told that they requested this land?
The Ramban simply explains that originally, it was only the tribe Reuven and Gad approached Moshe, as the Torah relates. Once they started dividing up the land, they realized that it was too big for just two tribes. Therefore, it was put out there for any other tribe to take a portion, if they so pleased. Some members of the tribe of Menashe volunteered, and were given a portion as well. The Ramban hypothesizes that perhaps the reason they were interested in this land is they had a large flock, similar to Reuven and Gad.
However, the Midrash provides a different, more surprising reason behind the tribe of Menashe’s inclusion. In the story of Yosef and his brothers, the former was viceroy of Egypt and in disguise. His brothers didn’t recognize him. As part of his plot to test his brothers’ loyalty, Yosef had his son Menashe plant his prized goblet in his brother Binyamin’s bag, to frame him as stealing from royalty. After sending the brothers home, Menashe chased after them and “found” the goblet. The brothers all tore their garments in mourning, fearing for Binyamin’s fate. Our Sages tell us that since Menashe caused the brothers to rend their garments, Menashe’s portion in the land of Israel was split in two .
This would appear to be a punishment. Rav Moshe Shternuch shlita points out that this shows us the depth of Hashem’s judgement. Even though Yosef was actually acting properly with his brothers, testing out their loyalty. Even though Menashe was following his father’s orders. Despite all this, at the end of the day, Yaakov’s sons were pained, and this was paid back by Menashe’s descendants. As a result, their portion in the land was split, and the tribe itself was divided into two.
However, at the same time, Hashem’s punishment served to correct the underlying flaw that caused all this. The reason why Yosef had to frame his brothers and cause them pain was due to the inherent strife and discord between the brothers. Having Reuven and Gad on the other side of the Jordan River, separated from the rest of the tribes, was surely going to cause that friction to continue. Menashe, although split, would maintain their familial connection. Having them on both sides of the river ensured that communication and fraternity would continue positively between all the tribes. Menashe, who caused pain to his brothers, was the ultimate medium to rectify the discord between them.
 Based on my own research and collection of sources
 Numbers 32:33
 The Torah says “half”, but it means a (small) portion (Ramban ad. loc.); Cf. Targum Onkelos and Targum “Yonasan” ad. loc., who translate חצי as “half”, seemingly taking the Torah at face value
 Ramban loc. cit.
 Bereishis Rabbah 84:20, brought by Moshav Zekeinim ad. loc., Hadar Zekeinim and Chizkuni to Genesis 44:13 (none of which mention it’s a Midrash). It also appears in Midrash Tehillim 10:3; Midrash Seichel Tov, Midrash Lekach Tov, and Midrash HaGadol to Genesis 37:34; Yalkut Shimoni Vayeishev § 143. Moshav Zekeinim actually says more like the Ramban, that the land was too big, but they answer why specifically Menashe was chosen by quoting the Midrash
 Yefeh Toar ad. loc., quoted by Eitz Yosef ad. loc., says this is from Bereishis Rabbah 91:8, brought by Rashi to Genesis 42:23; Targum “Yonasan” to Genesis 44:1
 What’s interesting is the Malbim to Joshua 17:1 says that Chazal had a tradition that Menashe’s portion was split because his father Yosef caused the sons of Yaakov to rend their garments. He then is bothered why wasn’t Yosef’s other son Efraim punished, and answers that Menashe was the firstborn. All the above Midrashim say that it was Menashe’s fault, which would explain why he was punished. However, see following note. The Midrash does say that Yosef caused the brothers to rend their garment, but it says that he was punished by having his descendant Yehoshua tear his garments (Joshua 7:6). Perhaps the Malbim put these two statements together.
 Yefeh Toar to Bereishis Rabbah 84:20 says that even though Menashe was just following his father’s orders, we have a rule מגלגלין חובה על ידי חייב (Shabbos 32a), meaning it’s not by chance that it ended up happening through Menashe. He is also bothered that even though the Midrash said earlier that Yehoshua tore his garments as punishment for Yosef causing his brothers to tear their garments, and he was from Menashe, still, that wasn’t enough to punish both Yosef and Menashe. Therefore, Menashe’s portion was split. צ”ע, as Yehoshua was from Efraim, not Menashe. Interestingly, I did find another source that says this: Sechar Sachir parshas Vayeishev p. 139 by Rav Yissachar Meir, Rosh Yeshiva of Yeshivas HaNegev. However, I subsequently discovered that the Neizer HaKodesh to Bereishis Rabbah loc. cit. explicitly accuses the Yefeh Toar of making a mistake
 Neizer HaKodesh loc. cit. explains that it’s not that it was against their will. They were interested and willing to join Reuven and Gad. Rather, Hashem brought it about that they would be interested, as a form of retribution
 Ta’am V’Da’as to Numbers 32:33