Abraham provided for the basic necessities of Hagar and Ishmael as much as Hagar could carry and sent them away. And in that moment Abraham secured the future of the promise of God. God would make him into a great nation. Isaac was the child of promise. The promises of God were all coming true.
We weep because we love them and we weep because life will not be the same without them. We weep for ourselves who are left behind and we weep for a life that now has one important person missing. Our weeping is not a lack of faith, it is an expression of our love.