There are many reasons that Chazal bring as why Amalek attacked Yisrael. In our parsha it is derived from the juxtaposition of the prohibition of having inaccurate weights and measurements and the coming of Amalek to destroy Am Yisrael. When it comes to inaccurate weights and measurements the Torah says the prohibition is carrying two apparently identical weights אבן ואבן yet one is big and one is small. The same is to keep two seemingly identical dry measurements איפה ואיפה yet one is big and one is small. אבן שלמה וצדק יהיה לך Only one perfect and correct stone. Historically, dishonest merchants used a heavy stone when buying goods (taking more) and a light stone when selling (giving less), or used a fake second stone to fool inspectors. False weights are sheker and so is Amalek.
With the prohibition of inaccurate weights the Torah prohibits them to be in your house even though you do not use them. This is strange since we don't find this by other Torah issurim such as the possession of chazir in your house even though you do not intend to eat it.
In Parshas Beshalach the reason given is רפידים which Chazal explain that this location represents their lack of learning Torah רפו ידיהם מן התורה they weakened their hands from the Torah. Also in that parsha, Yisrael had a loss of emunah in Hashem היש ה' בקרבנו אם לא and because of this they were punished with Amalek battling to annihilate them. If we take a deeper look at these reasons we will find a common theme in all three.
When Am Yisrael fights with Amalek in Parshas Beshalach, Moshe'a hands became heavy so Ahron and Chur took a stone and placed it by Moshe to sit on it and they held up his hands. Why did they take a stone for Moshe to sit on? It was his hands that became fatigued and they were supported by Ahron and Chur who solved the problem of heavy hands. What purpose did the stone serve in the war?
We are told that there are four different levels to understand Torah pshat derush remez and sode. We would like to answer these questions utilizing the deeper levels. The root word for weights and scales שקל which is gematria .נפש We see from this that weighing the pros and cons of a moral decision that one has to make is also included in the deeper meaning of accurate weights of a person's daas.
There are two types of daas that one could possess: Daas Torah and Daas Nachash, (Bereishis Rabba 19,9), one being truthful and the other inaccurate which leads one to act against Hashem's wishes. The more one involves himself with the learning of Torah the more he possesses Torah Intelligence. With T.I. if one comes to a point of spiritual uncertainty and doubt he has a greater chance of choosing Hashem's wishes. However, if his mind is polluted and dominated by culture intelligence which will shape his spiritual decisions, the chances of producing a morally correct outcome is very slim.
Amalek is gematria ספק doubt. Their tumah is to arouse in a Yid to doubt an absolute truth. When Yidden left Mitzrayim the world was petrified to start up with Yisrael. Once Amalek jumped into this hot bath he achieved his goal of removing the fear from the once unthinkable of not attacking Yisrael. In other wards he altered the psyche of all nations to now be only in "doubt" concerning that "perhaps bad would happen to them if they make war with Yisrael. By weakening their commitment to learning Torah daily Yisrael allowed Amalek's presence to enter their thinking and hearts which resulted into their questioning whether Hashem resided amongst them or not.
A Yid must also be on the alert that Amalek always seeks to penetrate the barrier of one's Torah intelligence and plant a malware inside your thinking process and attempt to hijack your daas and put the Nachash in charge of decisions. That is why the Torah says one should not have a scale of intelligence that is not accurate which means that he should completely avoid any infusion of Nachash intelligence in his head even if he doesn't use it for processing decisions. He must strive to have a non polluted mind, clear from any alien and deceitful knowledge. One never knows when Amalek will strike you with his doubts and you could fall prey chas veshalom to his way of thinking and abandon the Torah's way.
As we explained above the false weights are described as two weights one big and one small. By having perfect weights which means Torah intelligence without influence from a goyish lifestyle infiltration, one is rewarded with long life. To defeat Amalek one needs to fortify the "one stone" perfection of wisdom ראשית חכמה יראת ה' . This was the symbolic taking of one אבן to support Moshe and Klal Yisrael in their battle against Amalek. If one possesses inaccurate weights he conveys a lack of emunah in Hashem my making it appear as if Hashem does not see and know what you are doing. The passuk says of Moshe with one stone ויהי ידיו אמונה. Moshe conveyed emunah with his hands. Having two stones אבנים is gematriah אמונה עה"כ. You are the opposite of emunah .זה לעומת זה If we can eradicate Amalek's influence from our heads and hearts we can rid him from the world and bring about the revelation of complete Malchus Shamayim.