Gemara

Yehoshua told Bnei Yosef "Im Am Rav Atah Ale Lecha ha'Harah" - (since you are numerous,) conceal yourselves in forests, lest an Ayin ha'Ra prevail over you.

They responded 'we descend from Yosef, over whom Ayin ha'Ra does not prevail. In the Berachah to Yosef, it says "Alei Ayin (he has grace in the eyes of all who see him)."'

(R. Avahu): This may be read 'Olei Ayin' (his descendants prevail over Ayin ha'Ra).

(R. Yosi bar Chanina): We can learn from "v'Yidgu la'Rov" - just like fish are covered in water, so no Ayin ha'Ra prevails over them, also Ayin ha'Ra does not prevail over Yosef's seed.

Berachos 20a: Alternatively, since Yosef's eye did not want to look at what was forbidden to him (Potifar's wife), Ayin ha'Ra does not rule over him (or his seed).

Rav Huna wrote 70 Sifrei Torah. In only one Sefer, the dimensions matched (the height equaled the circumference). Rav Acha bar Yakov wrote one Sefer Torah; the dimensions matched. Rabanan were envious, and Rav Acha died.

Rav Chanina brei d'Rav Ika saw Rav Papa and Rav Huna brei d'Rav Yehoshua and said 'to me, you are like 600,000 Yisre'elim. For seeing you, I can bless "blessed is He who knows secrets."'

Rav Papa and Rav Huna exclaimed 'are you such a Chacham?!' They put their eyes on him, and he died.

Bava Metzi'a 84b: Rebbi and R. Elazar b'Rebbi Shimon used to sit on the ground in front of (older) Rabanan, who sat on benches. Rabanan learned much from them, and made benches for them to sit on.

R. Shimon ben Gamliel: I have one precious son (Rebbi). Do you seek to make me lose him (through Ayin ha'Ra)?

They returned Rebbi to the ground. R. Yehoshua ben Korchah exclaimed 'should R. Elazar, who has no father (to guard him from situations of Ayin ha'Ra), die?!'

107b (Rav): "V'Hesir Hash-m Mimecha Kol Choli" refers to Ayin ha'Ra;

Rav went to a graveyard and said that 99 of every 100 died from Ayin ha'Ra. Only one died normally.

Sanhedrin 93a (Rav): Chananyah, Misha'el and Azaryah died (after they refused to bow to the image and a great miracle was done for them) due to Ayin ha'Ra.

Avos 2:11 (Mishnah - R. Yehoshua): Ayin ha'Ra, Yetzer Ra and hatred of people remove a person from the world.

Rishonim

R. Yonah (Avos 2:11): Ayin ha'Ra is one who is unhappy with his portion and looks at the portion of one richer than himself. He causes evil to himself, and, scientists say, also to the one he envies. He himself becomes short of breath; this is how it removes him from the world.

Milchamos Hash-m (Berachos 44a): R. Chanina had awesome Chachmah to see from the faces of Rav Papa and Rav Huna that they contained all forms of wisdom, like 600,000 Yisre'elim. He died from Ayin ha'Ra.

Chazon Ish (Likutim Bava Basra 21 for Daf 14 DH Sham Yahavu): A basis of the world is that man's thoughts motor hidden forces; they can destroy physical things. When people are impressed by success, this endangers it. In any case everything is from Shamayim. Something will be lost only if this was decreed. A decree is fulfilled through Ayin ha'Ra. Rav saw that 99 out of 100 died through Ayin ha'Ra; this was the agent for the decree of Yom Kipur. The time had arrived for Rav Acha bar Yakov to die. Hash-m caused it to happen through Rabanan's astonishment at his success. R. Shimon ben Gamliel was concerned lest Rebbi die through Ayin ha'Ra, for the Satan prosecutes at times of danger; man is judged every day. Also, sometimes the judgment on Yom Kipur is that one will be left to nature, and a miracle will not be done for him. The Ayin ha'Ra of Rav Papa and Rav Huna killed R. Chanina. If someone is at a high level, all his faculties are greater, including his eye.

Poskim

Shulchan Aruch (OC 141:6): Two brothers, or a father and son can be called to read from the Torah one after the other. We refrain only due to Ayin ha'Ra.

Beis Yosef (DH Kasuv): Orchos Chayim (Hilchos Sheni v'Chamishi 26) forbids because they cannot testify together, and it says "Edus Hash-m Ne'emanah". The Kolbo (20:10b) and Mordechai (Hilchos Ketanos 968) cite the Tashbatz (190), who says that we refrain only due to Ayin ha'Ra.

Gra (10): It is due to Ayin ha'Ra. Women and children can count towards the required number of Aliyos, even though they cannot testify.

Be'er Heitev (5): Shirei Keneses ha'Gedolah forbids a man and his grandson. The Pri Chodosh disagrees. L'Chatchilah we do not allow one to read after his brother or father or son, but if he already went up, he does not go down.

Mishnah Berurah (19): This applies to paternal or maternal brothers. When necessary, a man and his grandson can be called consecutively.

Hagahos in Birkei Yosef (4): The Birkei Yosef (in Machazik Berachah 5) says that we do not call one and his grandson consecutively if they are concerned for this. We do not call brothers consecutively even if they are not concerned.

Kaf ha'Chayim (27): When there is no custom to be lenient, one should be stringent, for we are more stringent about danger than Isur. The concern is only for a son's son, who bears the same name, but not for a daughter's son.

Kaf ha'Chayim (30): Some places do not call brothers even not consecutively. This is not the custom of Eretz Yisrael, Miztrayim or Turkey.

Shulchan Aruch (ibid.): Even if one reads Shevi'i and the other reads Maftir, we do not call the latter by his name due to Ayin ha'Ra.

Source: Maharil Hilchos Kri'as ha'Torah, cited by Darchei Moshe 3.

Mishnah Berurah (20): This is on Shabbos, when they read from the same Sefer Torah, but not on Yom Tov. We always permit if the Maftir is a minor.

Kaf ha'Chayim (33): Some say that since Kaddish is not a sufficient break when they read from one Sefer, we forbid even from a second Sefer. Some say that Kaddish is a sufficient break, and permit even from one Sefer. We follow the Rema.

Mishnah Berurah (21): Where the custom is to call the Maftir Stam (without mentioning his name), it is permitted. Where he is called by name, one should not call a brother Stam, for this arouses attention.

Kaf ha'Chayim (32): Where a Mi she'Berach is made for the Oleh and his name is mentioned, we are concerned even if he was called to read Stam.

Acharonim

Ben Yehoyada (118a DH Eitzah): Why did the Gemara say about Bnei Yosef's request for more land that it was a good counsel to avoid Ayin ha'Ra? It should have said so about Yehoshua's answer! Rather, it is good counsel to request or bless Hash-m when mentioning one's good fortune, like they said "we have many people... Hash-m has blessed us to this point."