Luke likely had would have given him a chance. In fact, when Luke had been here, he had actually given him a chance. But Anakin didn't feel that just because Luke had given him a chance that Leia needed to as well. He was glad that she seemed to be trying to, though. Because he wanted to get to know his daughter, and that would be impossible if she hadn't been.
He offered Leia a smile as he entered her apartment. "That is perfectly alright," he told her. "I would like a drink, though." While it wasn't as hot here as it was on Tatooine, it was still rather hot. The humidity is what got to him. They didn't have humidity on tatooine.
Artoo beeped mournfully when he was told he couldn't have a drink, and Anakin laughed softly at him. "You can't even drink, Artoo."