Smother him with attention, as that's all he craving.He's six so he knows he shouldn't really be doing this and doubtless inwardly he feels all of those nasty negative guilty emotions that little kids feel and as anyone whose ever expereinced jealousy will tell you it's an awful feeling and too much for a little lad to deal with easily.
IMHO you need to devote (very obviously and enthusiastically) much more attention to him. Let him see how special he is to you and ask for his help and reward him for it. Thank him and treat him in a much more grown up manner and shift the attention from the little one for a while as much as you can.Make the clear distiction between them. He is older and special in his own way. She is littler and needs HIS help, protection which you then reward him for in a really enthusiastic way.
We've got a very large family and this method really works for us.