You've grown up. You know everything I can tell you. If you're still seeking out May, she must have qualities I've never had a chance to observe I wouldn't want to be shut out of your life, whatever you do. I'm rather short on sons.
When Willie confronts his mother with his desire to make May Wynn his wife, she responds in this way. Coming into the discussion, Willie thought that he was making a choice between his wife and his mother. Instead, he learns that his mother has come to terms with the fact that he has become a man, and that she only wants what is best for her son. Willie's happiness and their continuity as a family has become Mrs. Keith's priority.