Lyric discussion by Bleda 

Cover art for Dilate lyrics by Ani DiFranco

I would suggest that, as Ani sings it, Dilate refers to the lack of excitement that this person/lifestyle/character trait gives her. When put into an exciting/stressful situation, our heart rate rises and we get tunnel vision. When this subsides, our eyes "dilate", as MurryHam described. That is to say, as situations become less adverse, our eyes dilate.