This statement was made by Annie Dillard in her essay, "Living like the weasels".
By the statement, "I would like to live as I should as the weasel lives as he should", the author means that, like the weasel, she would live as she is meant to, focus on her goals, and will never give up on whatever she feels she is meant to do.
She expresses her great admiration for the weasel’s way of life; a life that is lived out of pure necessity, and not by choice, bias, or motive as humans do.
She explains in her essay that If humans could understand the purity in the mindlessness of the weasel’s way of life, each person could live how they wanted, unrestricted by imposed human behavior, societal norms and expectations.