hi snobbish,
looking at your situation, it is obvious he likes you being around
him.
i feel that it is good and important that your direct superior
enjoys your presence. since you only started working, it is
understandable that he is curious about you (most ppl like new
things). would you rather want your direct superior hates you,
dumps you all the work, hard to take leave etc?
a little advice i can offer would be to, from time to time,
mentioned to him that you feel stress and sometimes loses sleep
when hanging out with him (your boss) too often, that you hope to
have just a little break from work related stuffs especially during
lunch hours, after office hours.
or when you're with him, read books, newspapers etc, keep your
conversations with him to the minimal, make him feel bored or let
him understand you have things you want to do during your
break.
also please appreciate the fact that he likes you, and build a
friendship on it. don't be sick of him.
hope i've been of help. 
