In Act II, Scene 2, Mama puts Walter in charge of all of the money. Why do you think that she does that?

I think Mama put Walter in charge of the money because she thought that the knowledge of her trusting him would cause him to use it wisely, and as she asks. She does not trust him, and Walter believed this to be so but was not certain. As a result, her trust is highly valued by him, because he does not see the emotion translate into something tangible often. Mama knew Walter wasn't going to spend the money wisely even if he had it because he puts his emotions before logical thought. So, if she made him think she trusted him, then that might counteract his thoughtless actions because of the pressure that knowledge would put on him.

However, Mama's calculated risk was wrong. Walter does not value Mama or her opinions. He only values her when she has something to offer him that he wants, such as money. As a result, Mama's trust is shocking, but not of great importance to him. It is not enough to make him think through his decision, otherwise he would have put the money in the bank, not given it to Woody. I don't think he intentionally was illogical. That is simply how he is, and Mama's false trust couldn't change that no matter how good of an actress she may be.