Is anxiety connected to the three unwholesome roots? I have read that anxiety/worry is unwholesome. Is this because it is a form of aversion, one of the three unwholesome roots, or something else?
Anxiety/worry taken together are one of the five "nīvarana" in the Buddha Dhamma. "Nīvarana" are states of mind that conceals, hinders, covers, prevents the understanding of the true nature things.

Restlessness (uddhacca) and worry (kukkucca)


  Restlessness (uddhacca) has the characteristic of disquietude,
  like water whipped by the wind. Its function is to make the mind
  unsteady, as the wind makes a banner ripple. It is manifested as
  turmoil. Its proximate cause is unwise attention to mental disquiet.
  
  Kukkucca is worry or remorse after having done wrong. Its
  characteristic is subsequent regret. Its function is to sorrow over
  what has and what has not been done. It is manifested as remorse. Its
  proximate cause is what has and what has not been done (i.e. wrongs of
  commission and omission).


Bhikkhu Bodhi 


  Is this because it is a form of aversion, one of the three unwholesome
  roots, or something else?


Yes, and could also be caused by the other 2 unwholesome roots as well. Anxiety can be due to a state of conflict. The mind in a fight or flight situation. Or caused by a state of desire, an expectation, or a state of ignorance. 

Restlessness and worry are painful states of existence. 

You can find more about the 5 Hindrances here and recommendations on how to overcome them. 

May you be happy.