Bilaam's threat to Klal Yisroel registers as unique in many ways. We are enjoined, "My nation remember what Balak schemed against you and what Bilaam responded...in order that you recognize G-d's kindness" (Michah 6.) Similarly, "Hashem turned his curses into blessings, for He loves you" (Devarim 26.)
To the naked eye it seems that Bilaam's threat falls far short of those of Pharaoh, Amalek, and Sichon, all of whom employed physical force against us and actually hurt and oppressed us. Bilaam's curses, by comparison, are just a form of prayer, and if Hashem doesn't want to listen to those prayers, why are they so significant?
Bilaam's own status is also unclear. He is depicted as being a prophet (Sanhedrin 106a), similar to, or in the order of, Moshe (Bamidbar Rabba 14:19.) Was Bilaam good or evil? If he was evil, how could something as "spiritual" as prophecy become subverted for the bad?
Bilaam is described as a "sorcerer." We really have little understanding of what this is since we have no personal experience today with magic, etc. However, we will need to understand what the evil in magic is - at least conceptually - if we are to have any understanding of "parshas Bilaam".
We understand the natural order in our physical universe. It is governed by immutable laws that always are in affect unless Hashem chooses to override them, as in the case of miracles. There is a higher stratum of existence that transcends our physical world, which we call the spiritual world. It is not bound by the constraints of the familiar laws of nature, but it is also not a world devoid of structure and mechanism. The Maharal explains many times (especially in Gevuros Hashem) that there is an order and structure to miracles. This order is why the Talmud has disputes about miraculous events such as the stopping of the sun at Givon and its duration. Underlying the dispute are different understandings of the particular nature, not physical nature but metaphysical nature, of that miraculous event.
Another area where this type of understanding manifests itself is in the descriptions of the Yom Hadin, and the process of din in general. We are told about the order of who is judged first, what time of the day is most auspicious, etc. Even without plumbing and penetrating to the depths of understanding these details of din, we see that they clearly indicate that the spiritual world has structure, and only in the most extreme cases will Hashem override that order and structure (i.e. maavir al midosav.)
Because there are strata of spirituality that have their own inherent structure and whose system of functioning Hashem does not look to override on a regular basis, this structure too can be perverted and misused. This is the realm of magic, which is the tapping into some spiritual level and perverting it. The power may be spiritual, but rather than being used to bind a person to Hashem, it is being used to break away from Hashem.
That is the reason why "magic" is so destructive. Just as a friend who turns against you is so much more dangerous than someone who was always an enemy because he knows all your vulnerabilities, so too a person who has heightened spiritual sensitivity and misuses it is a much more dangerous adversary. Although Hashem can, of course, do as He wishes and prevent a wicked person from leveraging such spiritual resources just as He could prevent the wicked from making use of physical resources, He desired that the world run within a system - be it the physical world or the "supernatural world". Therefore, a person who is part of a more spiritual stratum has the choice and ability to do much good, and commensurately much evil.
Bilaam was the most knowledgeable and spiritually sensitive of Klal Yisroel's enemies, and this is precisely why he was the most dangerous. He could attack Klal Yisroel's deepest spiritual connection to Hashem and tried very hard to do so. Rashi describes Balak's choosing of Bilaam as a desire to utilize Israel's own strength (i.e prayer) against them. Bilaam was also shrewd enough to realize that seducing Israel to sin would do more to destroy them than a physical assault. Therefore, to protect Klal Yisroel, Hashem suspended the normal mechanisms of the spiritual world. This suspension goes against the deepest wishes of how HKB"H wants the world to generally run, and thus doing so was an expression of the love that He has for Klal Yisroel.
We have a hard time really getting a feel for these lofty concepts and battel grounds because we are removed from the experiences of "magic", etc. But these ideas are helpful if they can provide insight into some relatively contemporary phenomena.
Klal Yisroel has always had members who drifted away because of a desire for physical indulgences. It is sad to see anyone in Klal Yisroel lost, but that type of drifting is not the ultimate tragedy. Let us look at a much deeper tragedy in the annals of Klal Yisroel - the Jewish communists. Here were people far more spiritual than the fellow who wanted to live the good life in Paris and checked out. These communists were people whose deepest feelings of care for the downtrodden moved them. Their sense of injustice in the world fired their soul. They were willing to live a life of total denial and give up their lives for "the cause". Are these not "spiritual" qualities? Yet these "spiritual" qualities were turned against Hashem and they produced some of the most destructive eras in the annals of Klal Yisroel! The relentless persecution of Yiddishkeit, and its almost total obliteration in the Soviet Union, could only have happened because the driving force was "spiritual" rather than material.
This parsha teaches us that spirituality, while by its very nature is closer to the Divine than physicality, is still not automatically good. It all depends on where those strength and abilities are aimed. If it is focused on serving as a bridge to Hashem then it is the "good" itself. But if chas v'shalom it is used to attack Hashem, it is devastating.