What are the connotations of "Baruch mi'Banim Asher!"?
Rashi #1 (citing the Sifri): It means that none of the sons of Ya'akov (the tribes) is blessed with sons like Asher. 1
Rashi #2 (citing the Midrash Rabah): It means that he is blessed with beautiful daughters 2 (who marry kings who have been anointed with the anointing oil - Rashi in Yevamos, 102a).
Ramban #2 (citing the Sifri) 5 : None of the tribes was blessed like Asher regarding the attributes mentioned in Divrei ha'Yamim 1, 7:40.
Ramban #3: Asher is blessed by the other tribes and accepted by them, because their land is rich in produce and it provides the other tribes with all the delicacies that are fit for the king's table. 6
Ramban #4 (citing the Midrash Rabah): The tribe of Asher was unique inasmuch as they never had to lodge in inns, because they inherited palaces. 7
Targum Onkelos: Asher will share in the blessings of the other tribes. 8
Da'as Zekenim and Rosh: Asher is blessed by the other tribes and accepted by them, because their land is rich in oil, which they supply to the other tribes.
Seforno: Asher is blessed by the other tribes and accepted by them. 9
In what way was Asher favored by his brothers?
Rashi: Because he provided them with Shemen Anpikinun - olive-oil that is manufactured from olives that were not yet one-third grown 1 and delicacies, 2 in return for which they provided Asher with produce.
Ramban: Refer to 33:24:1:3, 33:24:1:5 & 33:24:1:6*.
Targum Yonasan: By providing them with food during the Sh'mitah-year. 3
Sifri and Yalkut Shimoni: After Asher revealed that Reuven switched Ya'akov's bed, his brothers excommunicated him 4 for allegedly falsely slandering their oldest brother. After Reuven admitted, his brothers permitted the Niduy and were reconciled with him.
Pane'ach Raza: Moshe Davened that the Niduy (that his brothers imposed on him for revealing Reuven's sin) should be repealed.
What does the Pasuk mean when it states that Asher will dip his feet in oil?
Rashi #1: It refers to the fact that Asher's land produced (olive) oil like a fountain (providing them with sufficient oil to dip their feet in. 1
Seforno: Refer to 33:24:1:3*. And they achieve this by providing the other tribes with oil at a cheap rate. 2
Targum Onkelos: 'They will grow-up with the delicacies of kings. 3
Targum Yonasan: Their land will produce such an abundance of olives that they will produce sufficient oil to dip their feet. 4
Riva: Refer to 33:24:1:10*.
Refer to Bereishis, 49:20:1:1. Menachos 85b relates how, when the people of Ludki needed oil, they sent an agent to Gush Chalav - in Asher, to purchase oil for the entire city. A resident of Gush Chalav sold him sufficient oil for their entire city, worth 118,000,000 Dinarim. See also answer #4 and note.
Refer to 33:24:3:1*.
Menachos, 85b: The story is told of the men of Ludki who ran short of oil and who sent an emissary to purchase a million Sa'ah from a certain manufacturer in Asher. When he arrived ... the maidservant brought him a container of hot water to wash his hands and feet, followed by a golden bowl filled with oil to dip his hands and feet. See Torah Temimah, note 74 for explanation, and see the Gemara there for the conclusion of the story. Se also answer #1 and note.
Rashi (citing the Sifri) writes that none of the sons of Ya'akov was blessed with sons like Asher. See answer #3. But they were not the largest tribe?
Chizkuni, Riva and Rosh (citing R. Eliav): They had the largest increase (eleven thousand, nine hundred) from the first census to the census in Pinchas. 1
R. Chaim Paltiel #1: Perhaps Asher diminished proportionally less through the plague 2 than the other Shevatim.
R. Chaim Paltiel #2: Asher never stayed in the same lodging (house of his children). Even though a person should not change his lodging, he had more children than others [and wanted to visit each once]. Even though he had only four sons, he had many daughters, and lodged with their sons.
Chizkuni: Even though Menasheh increased more, Asher had the greatest increase of Ya'akov's sons. Riva: Generally, Efrayim is attributed to Yosef, only here Efrayim decreased).
He does not specify whether this refers to the plague after Korach, or in Shitim, or both. Either way it does not make Asher more numerous, since the latter census took place after both plagues (PF).