Oh, Alfred is just priceless there with that "Heh."
Yet again, Batstalking is love. Though I have to wonder how just watching her would be all that informative in letting him know she's "stable." But it is fitting that for Bruce: "I worry about Barbara sometimes and I hope she's doing all right now." = "I had better spy on Barbara."
And for Babs: "Bruce is spying on me. I should confront him and tell him to cut it out." = "Bruce is spying on me. I should let him continue until he decides to stop so that chastising him will have maximum impact and make him look like a fool."