“He (Amalek) happened upon you on the way, and he struck the weaklings who were straggling at the rear, when you were faint and exhausted, and he did not fear G-d.” (25:18)
Why do we reserve special hatred for Amalek, more so than for other nations which attacked us without provocation? R’ Yitzchak Ze’ev Soloveitchik z”l explains:
The Gemara (Bava Kama 79) says: Why is a burglar punished more severely than a robber? Because a robber (Gazlan) equates G-d with man [he is afraid of neither], while a burglar (Ganav) places G-d lower than man [he fears man more than he fears G-d, therefore he steals when man is not looking]
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R’ Soloveitchik explains: A burglar is a greater sinner than is a robber because a burglar has begun to think through the consequences of his action, but has stopped those thoughts before they can lead him to G-d. This is worse than a robber who has not thought out his actions at all–therefore he fears no one- but at least he has not snubbed G-d.
Similarly, had Amalek attacked Bnei Yisrael head-on, we would not fault him. However, by attacking only the weakest Jews, Amalek acknowledged that there is something to fear. Despite that, he showed that he did not fear G-d.