What Bible passages do Jehovah’s Witnesses use to support their view on free will? I’m given to understand Jehovah’s Witnesses hold to something similar to libertarian free will, the belief that a person’s choices are free from the determination or constraints of human nature and free from any predetermination by God.

Since I don’t understand the position very well, perhaps a brief explanation of the view would be helpful to me, but primarily my question is concerned with what argument can be made from the Bible for the JW view.
Anytime you want an official position of Jehovah's  Witnesses on a particular topic  use Google search  of your key words and add jw.org . I typed free will jw.org and numerous hits came up  that link you directly to Jehovah's Witnesses  official website.
The first one I think is a good fit to your question and I have included it below:


  What Does the Bible Say About Free Will? Is God in Control?
  
  God dignifies us with free will, the power to make decisions of our own rather than having God or fate predetermine what we do. Consider what the Bible teaches.
  
  God created humans in his image. (Genesis 1:26) Unlike animals, which act mainly on instinct, we resemble our Creator in our capacity to display such qualities as love and justice. And like our Creator, we have free will.
  To a great extent, we can determine our future. The Bible encourages us to “choose life . . . by listening to [God’s] voice,” that is, by choosing to obey his commands. (Deuteronomy 30:19, 20) This offer would be meaningless, even cruel, if we lacked free will. Instead of forcing us to do what he says, God warmly appeals to us: “O if only you would actually pay attention to my commandments! Then your peace would become just like a river.”—Isaiah 48:18.
  Our success or failure is not determined by fate. If we want to succeed at an endeavor, we must work hard. “All that your hand finds to do,” says the Bible, “do with your very power.”(Ecclesiastes 9:10) It also says: “The plans of the diligent one surely make for advantage.”—Proverbs 21:5.
  Free will is a precious gift from God, for it lets us love him with our “whole heart”—because we want to.—Matthew 22:37.
  
  Doesn’t God control all things?
  The Bible does teach that God is Almighty, that his power is not limited by anyone other than himself. (Job 37:23; Isaiah 40:26) However, he does not use his power to control everything. For example, the Bible says that God was “exercising self-control” toward ancient Babylon, an enemy of his people. (Isaiah 42:14) Similarly, for now, he chooses to tolerate those who misuse their free will to harm others. But God will not do so indefinitely.—Psalm 37:10. - JW .Org.


There are of course many more pages available on the subject if you wish to learn more about what Jehovah's Witnesses teach about free will vs predestination.