Anakin laughed softly at Leia's words, "Hey, now. Twins are rare, and Padme's first pregnancy... it wasn't like we could go around saying she was pregnant." They couldn't even go around saying that the two had married. Anakin had been (and still was) a Jedi Knight. Jedi were not supposed to have attachments, and marriage was definitely an attachment. So it had to be kept secret at the time.
"Luke would have been very happy," he decided. "From what I learned about him while he was here, he seemed like the sort who would be pleased that Padme is pregnant." Anakin, for one, was pleased with Padme's pregnancy. He was nervous, yes, but he was also pleased. He wanted a chance to raise a baby. He wanted to prove that he could be a good father.
He hoped he could be a good father. He didn't really have any sort of role model for that, now did he? He'd only had Shmi. Well -- Obi-Wan could have been considered a father, right? Though near the end, he was more of a brother figure.
"You think Jesse is older than he appears?" he asked. "Because, really, how could he have traveled the world at such a young age?" At least, many times over. "Perhaps he is," he said, considering. "There are stranger things than that, here."
And if Leia thought that Jesse wasn't dangerous or anything, Anakin would agree with her on that. He trusted her opinion.