"Anomalously" means "unusually," and anything or anyone who is "unusual" is "different." Human nature being what it is, those who are different are likely to be marginalized, and the use of the term "weird" serves the purposes of marginalization quite well. Not only are Anomalously Sensitive Persons different in having heightened levels of sensitivities, they are also likely to be different in purely objective criteria-- such things as hypopigmentation, Non-Right-Handedness, and having been born as one of a multiple birth. Their differences are such, however, that once they have mastered the challenges of being different, they are positioned to move on to become modern day shamans who help others to understand, and to live within the framework of a life-enhancing world view that, in early times, was known as "wyrd."
For those who want a more in-depth academic discussion of the subject, Ritchey's book, The H.I.S.S. of the A.S.P. is also recommended. It provides access to a questionnaire whereby you can determine if you are an Anomalously Sensitive Person.