What is the connection between weights and measures and Amalek?
Rashi: It teaches us that, if one cheats in weights and measures, one needs to worry about the enemy attacking. 1
Hadar Zekenim and Rosh (both in Pasuk18): Because Yisrael did not fear Hashem ("v'Lo Yarei Elokim" ? Pasuk 18) and had fraudulent measures, Amalek came. 2 This is the 'Mora' (fear) that the Gemara (Kidushin 33b) said is written about false measures.
Rashi: As the Pasuk writes in Mishlei, 11:1 "Moznei Mirmah To'avas Hashem", and immediately afterwards "Ba Zadon va'Yavo Kalon." Rosh (in Pasuk 18): Here, the previous Pasuk called false measures "To'avas Hashem". Even though the Pasuk in Beshalch Shemos, 17:8: attributes the attack of Amalek to the fact that they questioned Hashem's Presence among them - Refer to Shemos, 17:8:1:1 - cheating in weights and measures is also the result of a lack of Emunah.
The Da'as Zekenim (in Pasuk 18) also seems to explain it like this, but he says that "Veyareisa me'Elokecha" is written in connection with false measures. There must be a printing mistake. (PF)
What does the Mitzvah of "Zachor eis asher Asah l'cha Amalek" entail?
Ramban (citing the Sifri): It entails remembering what Amalek did by verbalizing it 1 , since the Torah adds - in Pasuk 19 - "Lo Tishkach!" - with reference to not forgetting in one's heart. 2
Refer to 24:9:2:3*. From the Ramban it is not initially clear how the Mitzvah is carried out - whether it is perhaps a Mitzvah to read this Parshah publicly - as the Mishnah writes in Megilah, 29a 'The second week, we read Parshas Zachor', and this also serves as an Asmachta (a support from the Torah) to read Megilas Esther. The Sefer ha'Chinuch (Mitzvah 603) however, states that, since the objective is not to forget, it will suffice to recite it once a year, or once every two or three years.
See Torah Temimah, note 200, who elaborates.
What are the implications of "ba'Derech be'Tzeischem mi'Mitzrayim"?
What is the reason behind the Mitzvah of remembering what Amalek did to us?
Ramban: To serve as a reminder to destroy Amalek and to blot out his name.
Sefer ha'Chinuch (Mitzvah 603): To take to heart that anyone who pains Yisrael is hated by Hashem, and his downfall will be commensurate with his evil and guile.