Why did Moshe concede to the request of the B'nei Gad and Reuven?
Seforno: In order to avoid Machlokes.
How does half of Menasheh suddenly appear on the scene?
Ramban: When Moshe realized that the land was larger than the two tribes were entitled to, he asked for volunteers to join them, and some families from Menasheh opted to join them. 1
Moshav Zekenim (citing Midrash Lekach Tov): When Moshe realized that Eiver ha'Yarden was larger than the flocks of B'nei Gad and B'nei Reuven needed, he gave some of it to Menasheh - specifically to Menasheh, because Menasheh caused his brothers to tear their garments, therefore his inheritance was torn [into two parts].
See also Oznayim la'Torah.
What are the connotations of "Chatzi Sheivet Menasheh"?
Ramban: It means a part of the tribe of Menasheh joined Gad and Reuven, not literally a half. 1
Ramban: Like we find in Melachim 1, 16:21. In fact, only two families out of eight - those of Machir and Gil'ad, both comprising men of war - remained in Eiver ha'Yarden, as the Pasuk relates in Yehoshua, 17b. See Ramban, who elaborates.
Why does the Torah not tell us how Moshe distributed Eiver ha'Yarden among the two and a half tribes?
Ramban: The Torah does not want to go into detail regarding these tribes, 1 since it does not describe how the territories of the other tribes was divided.
Ramban: Though in Devarim 3:13, for some reason, it does describe how Moshe gave the entire area of Argov and all of the Bashan to half the tribe of Menasheh. And in Yehoshua, 13:15 & 24, the Pesukim describe how Moshe distributed the rest of Eiver ha'Yarden among Reuven, Gad and half of Menasheh.
