What does "v'Asimah Eini Alav" mean?
Riva citing R. Tam, Ramban #1 (citing Ibn Ezra): To see him.
Ramban #2, Seforno and Targum Yonasan: He meant that he would have pity on him and look after him. 1
Tosfos ha'Shalem (5, citing Hadar Zekenim), Rosh: I (Yehudah) will supervise, lest you do evil to him. 2
Even if he did not say so expressly (Ramban). Hence their father need not worry about sending him down (Seforno).
Moshav Zekenim - Because we did like you commanded, will I abandon guarding him?! No, I will put my eye on him, and he will not veer from me and my supervision! (If so, the verse cites Yosef's words, Yehudah's comment, and the next verse is the brothers' response! - PF)
Why did Yehudah need to repeat what Yosef said to them?
Ohr ha'Chayim: You demanded to see Binyamin, and said that without this, we will not see your face. We told our father, and even so, he did not agree to send him until the grain was finished!
Malbim: You must fulfill your promise! 1
Ha'amek Davar: 'Simas Ayin' implies constantly overseeing him. Yosef's words show that he already desired, for some unknown reason, that Binyamin will be by him. This suggests that the episode with Yosef's cup is a ruse to fulfill Yosef's desire!
Where do we find that Yosef said, "v'Asimah Eini Alav"?
Rosh #1: Since Yosef asked for their small brother, this was in order to have mercy on him and benefit him. If not, why would they bring a youth to a strange land and separate him from his father who is so tied to him? 1
Yehudah said so about himself; he would watch over Binyamin. Refer to 44:21:1:3.
Hadar Zekenim: Yosef said, "bring your small brother to me and verify your words, v'Lo Samusu" (42:20). A Gezeirah Shavah teaches that "v'Lo Samusu" is Simas Enayim - "Lamah Namus l'Einecha" (47:19).
Riva says similarly. (Seemingly, Yosef demanded to see him to prove that they are not spies, and Yaakov consented because he had no other way to get food! - PF)